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Published online by Cambridge University Press:  28 April 2022

Ted Dobson
Affiliation:
Univerza na Primorskem, Slovenia
Aleksander Malnič
Affiliation:
Univerza na Primorskem, Slovenia
Dragan Marušič
Affiliation:
Univerza na Primorskem, Slovenia
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Symmetry in Graphs , pp. 474 - 496
Publisher: Cambridge University Press
Print publication year: 2022

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References

Ádám, A. 1967. Research problem 2–10. J. Combin. Theory, 2, 393.Google Scholar
Ahrens, W. 1901. Mathematische Unterhaltungen und Spiele. Teubner, Leipzig.Google Scholar
Alperin, J. L., and Bell, Rowen B. 1995. Groups and Representations. Graduate Texts in Mathematics, vol. 162. Springer-Verlag, New York.Google Scholar
Alspach, Brian. 1973. Point-symmetric graphs and digraphs of prime order and transitive permutation groups of prime degree. J. Combin. Theory Ser. B, 15, 1217.CrossRefGoogle Scholar
Alspach, Brian. 1979. Hamiltonian cycles in vertex-transitive graphs of order 2p. Pages 131–139 of: Proceedings of the Tenth Southeastern Conference on Combinatorics, Graph Theory and Computing (Florida Atlantic Univ., Boca Raton, FL, 1979). Congress. Numer., XXIII–XX. Utilitas Math., Winnipeg, MB.Google Scholar
Alspach, Brian. 1983. The classification of Hamiltonian generalized Petersen graphs. J. Combin. Theory Ser. B, 34(3), 293312.CrossRefGoogle Scholar
Alspach, Brian. 1989. Lifting Hamilton cycles of quotient graphs. Discrete Math., 78(1–2), 2536.CrossRefGoogle Scholar
Alspach, Brian. 2013. Johnson graphs are Hamilton-connected. Ars Math. Contemp., 6(1), 2123.CrossRefGoogle Scholar
Alspach, Brian, and Dobson, Edward. 2015. On automorphism groups of graph truncations. Ars Math. Contemp., 8(1), 215223.Google Scholar
Alspach, Brian, and Mishna, Marni. 2002. Enumeration of Cayley graphs and digraphs. Discrete Math., 256(3), 527539.Google Scholar
Alspach, Brian, and Parsons, T. D. 1979. Isomorphism of circulant graphs and digraphs. Discrete Math., 25(2), 97108.Google Scholar
Alspach, Brian, and Parsons, T. D. 1982a. A construction for vertex-transitive graphs. Canad. J. Math., 34(2), 307318.Google Scholar
Alspach, Brian, and Parsons, T. D. 1982b. On Hamiltonian cycles in metacirculant graphs. Pages 1–7 of: Algebraic and Geometric Combinatorics. North-Holland Math. Stud., vol. 65. North-Holland, Amsterdam.Google Scholar
Alspach, Brian, and Qin, Yusheng. 2001. Hamilton-connected Cayley graphs on Hamiltonian groups. European J. Combin., 22(6), 777787.CrossRefGoogle Scholar
Alspach, Brian, and Xu, Ming Yao. 1994. 1/2-transitive graphs of order 3p. J. Algebraic Combin., 3(4), 347355.CrossRefGoogle Scholar
Alspach, B., and Zhang, Cun Quan. 1989. Hamilton cycles in cubic Cayley graphs on dihedral groups. Ars Combin., 28, 101108.Google Scholar
Alspach, Brian, Durnberger, Erich, and Parsons, T. D. 1985. Hamilton cycles in metacirculant graphs with prime cardinality blocks. Pages 27–34 of: Cycles in Graphs (Burnaby, B.C., 1982). North-Holland Math. Stud., vol. 115. North-Holland, Amsterdam.Google Scholar
Alspach, Brian, Locke, Stephen C., and Witte, Dave. 1990. The Hamilton spaces of Cayley graphs on abelian groups. Discrete Math., 82(2), 113126.Google Scholar
Alspach, Brian, Marušič, Dragan, and Nowitz, Lewis. 1994. Constructing graphs which are 1/2-transitive. J. Austral. Math. Soc. Ser. A, 56(3), 391402.Google Scholar
Alspach, Brian, Conder, Marston D. E., Marušič, Dragan, and Xu, Ming-Yao. 1996. A classification of 2-arc-transitive circulants. J. Algebraic Combin., 5(2), 8386.CrossRefGoogle Scholar
Alspach, Brian, Morris, Joy, and Vilfred, V. 1999. Self-complementary circulant graphs. Ars Combin., 53, 187191.Google Scholar
Alspach, Brian, Chen, C. C., and Dean, Matthew. 2010. Hamilton paths in Cayley graphs on generalized dihedral groups. Ars Math. Contemp., 3(1), 2947.Google Scholar
André, Jorge, Araújo, João, and Cameron, Peter J. 2016. The classification of partition homogeneous groups with applications to semigroup theory. J. Algebra, 452, 288310.CrossRefGoogle Scholar
Antončič, Iva, Hujdurović, Ademir, and Kutnar, Klavdija. 2015. A classification of pentavalent arc-transitive bicirculants. J. Algebraic Combin., 41(3), 643668.CrossRefGoogle Scholar
Arezoomand, Majid, and Ghasemi, Mohsen. 2021. On 2-closed elusive permutation groups of degrees p2q and p2qr. Communications in Algebra, 49(2), 614620.Google Scholar
Artin, E. 1988. Geometric Algebra. Wiley Classics Library. John Wiley & Sons, Inc., New York. Reprint of the 1957 original, A Wiley-Interscience Publication.CrossRefGoogle Scholar
Aschbacher, M. 1984. On the maximal subgroups of the finite classical groups. Invent. Math., 76(3), 469514.Google Scholar
Babai, L. 1977. Isomorphism problem for a class of point-symmetric structures. Acta Math. Acad. Sci. Hungar., 29(3–4), 329336.CrossRefGoogle Scholar
Babai, L. 1978. Infinite digraphs with given regular automorphism groups. J. Combin. Theory Ser. B, 25(1), 2646.Google Scholar
Babai, László. 1979. Long cycles in vertex-transitive graphs. J. Graph Theory, 3(3), 301304.CrossRefGoogle Scholar
Babai, L. 1980. Finite digraphs with given regular automorphism groups. Period. Math. Hungar., 11(4), 257270.CrossRefGoogle Scholar
Babai, László. 1995. Automorphism groups, isomorphism, reconstruction. Pages 1447–1540 of: Handbook of Combinatorics, vol. 1, 2. Elsevier, Amsterdam.Google Scholar
Babai, László. 2015. Graph Isomorphism in Quasipolynomial Time. CoRR, arXiv: abs/1512.03547.Google Scholar
Babai, László. 2016. Graph isomorphism in quasipolynomial time [extended abstract]. Pages 684–697 of: STOC’16 – Proceedings of the 48th Annual ACM SIGACT Symposium on Theory of Computing. ACM, New York.Google Scholar
Babai, L., and Frankl, P. 1978. Isomorphisms of Cayley graphs. I. Pages 35–52 of: Combinatorics (Proc. Fifth Hungarian Colloq., Keszthely, 1976), Vol. I. Colloq. Math. Soc. János Bolyai, vol. 18. North-Holland, Amsterdam.Google Scholar
Babai, L., and Frankl, P. 1979. Isomorphisms of Cayley graphs. II. Acta Math. Acad. Sci. Hungar., 34(1–2), 177183.Google Scholar
Babai, László, and Godsil, Chris D. 1982. On the automorphism groups of almost all Cayley graphs. European J. Combin., 3(1), 915.Google Scholar
Baik, Young-Gheel, Feng, Yanquan, Sim, Hyo-Seob, and Xu, Mingyao. 1998. On the normality of Cayley graphs of abelian groups. Algebra Colloq., 5(3), 297304.Google Scholar
Baik, Young-Gheel, Feng, Yanquan, and Sim, Hyo-Seob. 2000. The normality of Cayley graphs of finite abelian groups with valency 5. Systems Sci. Math. Sci., 13(4), 425431.Google Scholar
Balaban, A. T. 1972. Chemical graphs, part XIII; Combinatorial patterns. Rev. Roumaine Math. Pures Appl., 17, 316.Google Scholar
Bamberg, John, and Giudici, Michael. 2011. Point regular groups of automorphisms of generalised quadrangles. J. Combin. Theory Ser. A, 118(3), 11141128.Google Scholar
Barber, Rachel, and Dobson, Ted. 2022. Recognizing vertex-transitive digraphs which are wreath products, double coset digraphs, and generalized wreath products. Preprint.Google Scholar
Bays, S. 1930. Sur les systèmes cycliques de triples de Steiner différents pour N premier (ou puissance de nombre premier) de la forme 6 n+1. Comment. Math. Helv., 2(1), 294306.Google Scholar
Bays, S. 1931. Sur les systèmes cycliques de triples de Steiner différents pour N premier de la forme 6 n + 1. Comment. Math. Helv., 3, 2241, 122–147, 307–325.Google Scholar
Beaumont, R. A., and Peterson, R. P. 1955. Set-transitive permutation groups. Canad. J. Math., 7, 3542.Google Scholar
Bermond, J.-C. 1978a. Hamiltonian decompositions of graphs, directed graphs and hypergraphs. Ann. Discrete Math., 3, 2128. In Advances in Graph Theory (Cambridge Combinatorial Conf., Trinity College, Cambridge, 1977).Google Scholar
Bermond, J.-C. 1978b. Hamiltonian graphs. Pages 127–167 of: Beinke, L.W., Wilson, R.J. (ed), Selected Topics in Graph Theory. Academic Press, London.Google Scholar
Bhoumik, Soumya, Dobson, Edward, and Morris, Joy. 2014. On the automorphism groups of almost all circulant graphs and digraphs. Ars Math. Contemp., 7(2), 487506.Google Scholar
Biggs, Norman. 1973. Three remarkable graphs. Canad. J. Math., 25, 397411.CrossRefGoogle Scholar
Biggs, Norman. 1979. Some odd graph theory. Pages 71–81 of: Second International Conference on Combinatorial Mathematics (New York, 1978). Ann. New York Acad. Sci., vol. 319. New York Acad. Sci., New York.Google Scholar
Biggs, N. L. 1981. Aspects of symmetry in graphs. Pages 27–35 of: Algebraic Methods in Graph Theory, Vol. I, II (Szeged, 1978). Colloq. Math. Soc. János Bolyai, vol. 25. North-Holland, Amsterdam-New York.Google Scholar
Biggs, N. L., and Smith, D. H. 1971. On trivalent graphs. Bull. London Math. Soc., 3, 155158.Google Scholar
Boben, Marko, Pisanski, Tomaž, and Žitnik, Arjana. 2005. I-graphs and the corresponding configurations. J. Combin. Des., 13(6), 406424.Google Scholar
Bollobás, Béla. 1998. Modern Graph Theory. Graduate Texts in Mathematics, vol. 184. Springer-Verlag, New York.Google Scholar
Bondy, J. A. 1972. Variations on the Hamiltonian theme. Canad. Math. Bull., 15, 5762.CrossRefGoogle Scholar
Bonnington, C. Paul, Conder, Marston, Morton, Margaret, and McKenna, Patricia. 2002. Embedding digraphs on orientable surfaces. J. Combin. Theory Ser. B, 85(1), 120.Google Scholar
Boreham, T. G., Bouwer, I. Z., and Frucht, R. W. 1974. A useful family of bicubic graphs. Pages 213–225. Lecture Notes in Math., Vol. 406 of: Graphs and Combinatorics (Proc. Capital Conf., George Washington Univ., Washington, D.C., 1973). Berlin: Springer.Google Scholar
Bosma, Wieb, Cannon, John, and Playoust, Catherine. 1997. The Magma algebra system. I. The user language. J. Symbolic Comput., 24(3–4), 235265. Computational algebra and number theory (London, 1993).Google Scholar
Bouwer, I. Z. 1968. An edge but not vertex transitive cubic graph. Canad. Math. Bull., 11, 533535.Google Scholar
Bouwer, I. Z. 1970. Vertex and edge transitive, but not 1-transitive, graphs. Canad. Math. Bull., 13, 231237.Google Scholar
Bouwer, I. Z. 1972. On edge but not vertex transitive regular graphs. J. Combin. Theory Ser. B, 12, 3240.Google Scholar
Brand, Neal. 1989. On the Bays–Lambossy theorem. Discrete Math., 78(3), 217222.Google Scholar
Breckman, J. 1956. Encoding Circuit. US Patent 2733432. Issued Jan 31, 1956.Google Scholar
Brouwer, A. E., Cohen, A. M., and Neumaier, A. 1989. Distance-Regular Graphs. Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 18. Springer-Verlag, Berlin.CrossRefGoogle Scholar
Burnside, W. 1897. Theory of Groups of Finite Order. Cambridge University Press.Google Scholar
Burnside, W. 1901. On some properties of groups of odd order. J. London Math. Soc., 33, 162185.Google Scholar
Burton, David M. 2010. Elementary Number Theory. Seventh ed. McGraw-Hill, New York.Google Scholar
Cameron, Peter J. 1981. Finite permutation groups and finite simple groups. Bull. London Math. Soc., 13(1), 122.Google Scholar
Cameron, P. J. (ed). 1997. Problems from the fifteenth British combinatorial conference. Discrete Math., 167/168, 605615.Google Scholar
Cameron, Peter J., Giudici, Michael, Jones, Gareth A., et al. 2002. Transitive permutation groups without semiregular subgroups. J. London Math. Soc. (2), 66(2), 325333.Google Scholar
Cara, Philippe, Rottey, Sara, and Van de Voorde, Geertrui. 2014. A construction for infinite families of semisymmetric graphs revealing their full automorphism group. J. Algebraic Combin., 39(4), 967988.Google Scholar
Castagna, Frank, and Prins, Geert. 1972. Every generalized Petersen graph has a Tait coloring. Pacific J. Math., 40, 5358.Google Scholar
Chao, Chong-yun. 1965. On groups and graphs. Trans. Amer. Math. Soc., 118, 488497.Google Scholar
Chao, Chong-yun. 1971. On the classification of symmetric graphs with a prime number of vertices. Trans. Amer. Math. Soc., 158, 247256.Google Scholar
Chen, C. C., and Quimpo, N. F. 1981. On strongly Hamiltonian abelian group graphs. Pages 23–34 of: Combinatorial Mathematics, VIII (Geelong, 1980). Lecture Notes in Math., vol. 884. Springer, Berlin.Google Scholar
Chen, C. C., and Quimpo, N. 1983. Hamiltonian Cayley graphs of order pq. Pages 1–5 of: Combinatorial Mathematics, X (Adelaide, 1982). Lecture Notes in Math., vol. 1036. Springer, Berlin.Google Scholar
Chen, Ya-Chen. 2003. Triangle-free Hamiltonian Kneser graphs. J. Combin. Theory Ser. B, 89(1), 116.CrossRefGoogle Scholar
Chen, Yu Qing. 1998. On Hamiltonicity of vertex-transitive graphs and digraphs of order p4. J. Combin. Theory Ser. B, 72(1), 110121.Google Scholar
Chvátal, V. 1972. On Hamilton’s ideals. J. Combin. Theory Ser. B, 12, 163168.Google Scholar
Conder, Marston. 2006. Trivalent (Cubic) Symmetric Graphs on up to 2048 Vertices. www.math.auckland.ac.nz/conder/symmcubic2048list.txt.Google Scholar
Conder, Marston. 2011. Trivalent Symmetric Graphs on up to 10000 Vertices. www.math.auckland.ac.nz/conder/symmcubic10000list.txt.Google Scholar
Conder, Marston, and Dobcsányi, Peter. 2002. Trivalent symmetric graphs on up to 768 vertices. J. Combin. Math. Combin. Comput., 40, 4163.Google Scholar
Conder, Marston D. E., and Marušič, Dragan. 2003. A tetravalent half-arc-transitive graph with non-abelian vertex stabilizer. J. Combin. Theory Ser. B, 88(1), 6776.Google Scholar
Conder, Marston, and Morton, Margaret. 1995. Classification of trivalent symmetric graphs of small order. Australas. J. Combin., 11, 139149.Google Scholar
Conder, Marston, and Nedela, Roman. 2007. Symmetric cubic graphs of small girth. J. Combin. Theory Ser. B, 97(5), 757768.Google Scholar
Conder, Marston, and Nedela, Roman. 2009. A refined classification of symmetric cubic graphs. J. Algebra, 322(3), 722740.Google Scholar
Conder, Marston D. E., and Žitnik, Arjana. 2016. Half-arc-transitive graphs of arbitrary even valency greater than 2. European J. Combin., 54, 177186.Google Scholar
Conder, Marston D., Li, Cai Heng, and Praeger, Cheryl E. 2000. On the Weiss conjecture for finite locally primitive graphs. Proc. Edinburgh Math. Soc. (2), 43(1), 129138.Google Scholar
Conder, Marston, Malnič, Aleksander, Marušič, Dragan, and Potočnik, Primož. 2006. A census of semisymmetric cubic graphs on up to 768 vertices. J. Algebraic Combin., 23(3), 255294.Google Scholar
Conder, Marston D. E., Potočnik, Primož, and Šparl, Primož. 2015. Some recent discoveries about half-arc-transitive graphs. Ars Math. Contemp., 8(1), 149162.CrossRefGoogle Scholar
Conder, Marston D. E., Estélyi, István, and Pisanski, Tomaž. 2018. Vertex-transitive Haar graphs that are not Cayley graphs. Pages 61–70 of: Discrete Geometry and Symmetry. Springer Proc. Math. Stat., vol. 234. Springer, Cham.Google Scholar
Conder, Marston, Zhou, Jin-Xin, Feng, Yan-Quan, and Zhang, Mi-Mi. 2020a. Edgetransitive bi-Cayley graphs. J. Combin. Theory Ser. B, 145, 264306.Google Scholar
Conder, Marston D. E., Hujdurović, A., Kutnar, K., and Marušič, D. 2020b. Symmetric Cubic Graphs Via Rigid Cells. https://doi.org/10.1007/s10801-020-00946-3.Google Scholar
Conway, J. H. 1971. More About Symmetrical Graphs. Talk given at the Second British Combinatorial Conference at Royal Holloway College.Google Scholar
Conway, J. H., Curtis, R. T., Norton, S. P., Parker, R. A., and Wilson, R. A. 1985. Atlas of Finite Groups. Oxford University Press, Eynsham. Maximal subgroups and ordinary characters for simple groups, With computational assistance from J. G. Thackray.Google Scholar
Conway, J. H., Sloane, N. J. A., and Wilks, Allan R. 1989. Gray codes for reflection groups. Graphs Combin., 5(4), 315325.Google Scholar
Coxeter, H. S. M. 1950. Self-dual configurations and regular graphs. Bull. Amer. Math. Soc., 56, 413455.Google Scholar
Coxeter, H. S. M. 1983. My graph. Proc. London Math. Soc. (3), 46(1), 117136.Google Scholar
Coxeter, H. S. M. 1986. The generalized Petersen graph G(24, 5). Comput. Math. Appl. Part B, 12(3–4), 579583. Symmetry: unifying human understanding, II.Google Scholar
Coxeter, H. S. M., and Moser, W. O. J. 1965. Generators and Relations for Discrete Groups. Second ed. Ergebnisse der Mathematik und ihrer Grenzgebiete, Neue Folge, Band 14. Springer-Verlag, Berlin.Google Scholar
Cuaresma, Maria Cristeta, Giudici, Michael, and Praeger, Cheryl E. 2008. Homogeneous factorisations of Johnson graphs. Des. Codes Cryptogr., 46(3), 303327.Google Scholar
Curran, Stephen J., and Gallian, Joseph A. 1996. Hamiltonian cycles and paths in Cayley graphs and digraphs – a survey. Discrete Math., 156(1–3), 118.Google Scholar
Curran, Stephen J., Morris, Dave Witte, and Morris, Joy. 2012. Cayley graphs of order 16p are Hamiltonian. Ars Math. Contemp., 5(2), 185211.Google Scholar
Dieudonné, Jean. 1980. On the Automorphisms of the Classical Groups. Memoirs of the American Mathematical Society, vol. 2. American Mathematical Society, Providence, RI. With a supplement by Loo Keng Hua [Luo Geng Hua], Reprint of the 1951 original.Google Scholar
Dixon, John D., and Mortimer, Brian. 1996. Permutation Groups. Graduate Texts in Mathematics, vol. 163. Springer-Verlag, New York.Google Scholar
Djoković, Dragomir Ž., and Miller, Gary L. 1980. Regular groups of automorphisms of cubic graphs. J. Combin. Theory Ser. B, 29(2), 195230.Google Scholar
Dobson, Edward. 1998. Isomorphism problem for metacirculant graphs of order a product of distinct primes. Canad. J. Math., 50(6), 11761188.Google Scholar
Dobson, Edward. 2000. Classification of vertex-transitive graphs of order a prime cubed. I. Discrete Math., 224(1–3), 99106.Google Scholar
Dobson, Edward. 2002. On the Cayley isomorphism problem. Discrete Math., 247(1–3), 107116.Google Scholar
Dobson, Edward. 2003a. On isomorphisms of abelian Cayley objects of certain orders. Discrete Math., 266(1–3), 203215. The 18th British Combinatorial Conference (Brighton, 2001).Google Scholar
Dobson, Edward. 2003b. On the Cayley isomorphism problem for ternary relational structures. J. Combin. Theory Ser. A, 101(2), 225248.Google Scholar
Dobson, Edward. 2005. On groups of odd prime-power degree that contain a full cycle. Discrete Math., 299(1–3), 6578.Google Scholar
Dobson, Edward. 2006a. Automorphism groups of metacirculant graphs of order a product of two distinct primes. Combin. Probab. Comput., 15(1–2), 105130.CrossRefGoogle Scholar
Dobson, Edward. 2006b. On the proof of a theorem of Pálfy. Electron. J. Combin., 13(1), Note 16, 4 pp. (electronic).Google Scholar
Dobson, Edward. 2008. On solvable groups and Cayley graphs. J. Combin. Theory Ser. B, 98(6), 11931214.Google Scholar
Dobson, Edward. 2009. On overgroups of regular abelian p-groups. Ars Math. Contemp., 2(1), 5976.Google Scholar
Dobson, Edward. 2010. The isomorphism problem for Cayley ternary relational structures for some abelian groups of order 8p. Discrete Math., 310(21), 28952909.Google Scholar
Dobson, Edward. 2012. The full automorphism group of Cayley graphs of . Electron. J. Combin., 19(1), Paper 57, 17.Google Scholar
Dobson, Edward. 2014. On the Cayley isomorphism problem for Cayley objects of nilpotent groups of some orders. Electron. J. Combin., 21(3), Paper 3.8, 15.Google Scholar
Dobson, Ted. 2016. On isomorphisms of Marušič-Scapellato graphs. Graphs Combin., 32(3), 913921.Google Scholar
Dobson, Ted. 2018. On the isomorphism problem for Cayley graphs of abelian groups whose Sylow subgroups are elementary abelian cyclic. Electron. J. Combin., 25(2), Paper No. 2.49, 22.Google Scholar
Dobson, Edward, and Kovács, István. 2009. Automorphism groups of Cayley digraphs of . Electron. J. Combin., 16(1), Research Paper 149, 20.Google Scholar
Dobson, Edward, and Malnič, Aleksander. 2015. Groups that are transitive on all partitions of a given shape. J. Algebraic Combin., 42(2), 605617.Google Scholar
Dobson, Edward, and Marušič, Dragan. 2011. On semiregular elements of solvable groups. Comm. Algebra, 39(4), 14131426.CrossRefGoogle Scholar
Dobson, Edward, and Morris, Joy. 2005. On automorphism groups of circulant digraphs of square-free order. Discrete Math., 299(1–3), 7998.Google Scholar
Dobson, Edward, and Morris, Joy. 2009. Automorphism groups of wreath product digraphs. Electron. J. Combin., 16(1), Research Paper 17, 30.Google Scholar
Dobson, Edward, and Morris, Joy. 2015. Quotients of CI-groups are CI-groups. Graphs Combin., 31(3), 547550.Google Scholar
Dobson, Edward, and Šajna, Mateja. 2004. Almost self-complementary circulant graphs. Discrete Math., 278(1–3), 2344.Google Scholar
Dobson, Edward, and Spiga, Pablo. 2013. CI-groups with respect to ternary relational structures: new examples. Ars Math. Contemp., 6(2), 351364.Google Scholar
Dobson, Ted, and Spiga, Pablo. 2017. Cayley numbers with arbitrarily many distinct prime factors. J. Combin. Theory Ser. B, 122, 301310.Google Scholar
Dobson, Edward, and Witte, Dave. 2002. Transitive permutation groups of prime-squared degree. J. Algebraic Combin., 16(1), 4369.Google Scholar
Dobson, Edward, Gavlas, Heather, Morris, Joy, and Witte, Dave. 1998. Automorphism groups with cyclic commutator subgroup and Hamilton cycles. Discrete Math., 189(1–3), 6978.Google Scholar
Dobson, Edward, Malnič, Aleksander, Marušič, Dragan, and Nowitz, Lewis A. 2007. Minimal normal subgroups of transitive permutation groups of square-free degree. Discrete Math., 307(3–5), 373385.Google Scholar
Dobson, Edward, Li, Cai Heng, and Spiga, Pablo. 2012. Permutation groups containing a regular abelian Hall subgroup. Comm. Algebra, 40(9), 35323539.Google Scholar
Dobson, Edward, Spiga, Pablo, and Verret, Gabriel. 2016. Cayley graphs on abelian groups. Combinatorica, 36(4), 371393.Google Scholar
Dobson, Ted, Hujdurović, Ademir, Kutnar, Klavdija, and Morris, Joy. 2020a. Classification of Vertex-Transitive Digraphs Via Automorphism Group. arXiv:2003.07894[math.CO].Google Scholar
Dobson, Ted, Muzychuk, Mikhail, and Spiga, Pablo. 2020b. Generalised Dihedral CI-Groups. arXiv:2008.00200[math.CO].Google Scholar
Doyle, John Kevin, Tucker, Thomas W., and Watkins, Mark E. 2018. Graphical Frobenius representations. J. Algebraic Combin., 48(3), 405428.Google Scholar
Doyle, P. G. 1976. On Transitive Graphs. Senior Thesis, Harvard College.Google Scholar
Du, Shaofei, and Marušič, Dragan. 1999. An infinite family of biprimitive semisymmetric graphs. J. Graph Theory, 32(3), 217228.Google Scholar
Du, Shaofei, and Wang, Li. 2015. A classification of semisymmetric graphs of order 2p3: unfaithful case. J. Algebraic Combin., 41(2), 275302.Google Scholar
Du, Shaofei, and Xu, Mingyao. 2000. A classification of semisymmetric graphs of order 2pq. Comm. Algebra, 28(6), 26852715.Google Scholar
Du, Shaofei, Malnič, Aleksander, and Marušič, Dragan. 2008. Classification of 2-arctransitive dihedrants. J. Combin. Theory Ser. B, 98(6), 13491372.Google Scholar
Du, Shaofei, Kutnar, Klavdija, and Marušič, Dragan. 2018. Hamilton cycles in vertex-transitive graphs of order a product of two primes, arXiv:1808.08553.Google Scholar
Du, Shaofei, Kutnar, Klavdija, and Marušič, Dragan. 2020. Hamilton cycles in primitive vertex-transitive graphs of order a product of two primes – the case PSL(2, q2) acting on cosets of PGL(2, q). Ars Math. Contemp., 19(1), 115.Google Scholar
Dummit, D.S., and Foote, R.M. 1999. Abstract Algebra. Prentice Hall, Upper Saddle River, NJ.Google Scholar
Dummit, David S., and Foote, Richard M. 2004. Abstract Algebra. Third ed. John Wiley & Sons, Inc., Hoboken, NJ.Google Scholar
Durnberger, Erich. 1983. Connected Cayley graphs of semidirect products of cyclic groups of prime order by abelian groups are Hamiltonian. Discrete Math., 46(1), 5568.Google Scholar
Eiben, Eduard, Jajcay, Robert, and Šparl, Primož. 2019. Symmetry properties of generalized graph truncations. J. Combin. Theory Ser. B, 137, 291315.Google Scholar
Elspas, Bernard, and Turner, James. 1970. Graphs with circulant adjacency matrices. J. Combin. Theory, 9, 297307.Google Scholar
Erdős, P., and Rényi, A. 1963. Asymmetric graphs. Acta Math. Acad. Sci. Hungar., 14, 295315.Google Scholar
Erdős, P., Ko, Chao, and Rado, R. 1961. Intersection theorems for systems of finite sets. Quart. J. Math. Oxford Ser. (2), 12, 313320.Google Scholar
Estélyi, István, and Pisanski, Tomaž. 2016. Which Haar graphs are Cayley graphs? Electron. J. Combin., 23(3), Paper 3.10, 13.Google Scholar
Euler, Leonard. 1766. Solution d’une Question Curieuse Qui ne Paroit Soumise a Aucune Analyse. Euler Archive – All Works. https://scholarlycommons.pacific.edu/euler-works/309.Google Scholar
Evdokimov, S. A., and Ponomarenko, I. N. 2002. Characterization of cyclotomic schemes and normal Schur rings over a cyclic group. Algebra i Analiz, 14(2), 1155.Google Scholar
Fawcett, Joanna B., Giudici, Michael, Li, Cai Heng, Praeger, Cheryl E., Royle, Gordon, and Verret, Gabriel. 2018. Primitive permutation groups with a suborbit of length 5 and vertex-primitive graphs of valency 5. J. Combin. Theory Ser. A, 157, 247266.Google Scholar
Fein, Burton, Kantor, William M., and Schacher, Murray. 1981. Relative Brauer groups. II. J. Reine Angew. Math., 328, 3957.Google Scholar
Feng, Y.-Q., and Kovács, I. 2018. Elementary abelian groups of rank 5 are DCI-groups. J. Combin. Theory Ser. A, 157(5), 162204.CrossRefGoogle Scholar
Feng, Yan-Quan, and Kwak, Jin Ho. 2007. Cubic symmetric graphs of order a small number times a prime or a prime square. J. Combin. Theory Ser. B, 97(4), 627646.Google Scholar
Feng, Yan-Quan, and Nedela, Roman. 2006. Symmetric cubic graphs of girth at most 7. Acta Univ. M. Belii Ser. Math., 3355.Google Scholar
Feng, Yan-Quan, and Wang, Kaishun. 2003. s-regular cyclic coverings of the three-dimensional hypercube Q3. European J. Combin., 24(6), 719731.Google Scholar
Feng, Yan-Quan, Wang, Kaishun, and Zhou, Chuixiang. 2007. Tetravalent half-transitive graphs of order 4p. European J. Combin., 28(3), 726733.Google Scholar
Feng, Yan-Quan, Hujdurović, Ademir, Kovács, István, Kutnar, Klavdija, and Marušič, Dragan. 2019. Quasi-semiregular automorphisms of cubic and tetravalent arc-transitive graphs. Appl. Math. Comput., 353, 329337.Google Scholar
Feng, Yan-Quan, Kovács, István, Wang, Jie, and Yang, Da-Wei. 2020. Existence of non-Cayley Haar graphs. European J. Combin., 89, 103146, 12.Google Scholar
Folkman, Jon. 1967. Regular line-symmetric graphs. J. Combin. Theory, 3, 215232.Google Scholar
Foster, Ronald M. 1988. The Foster Census. Charles Babbage Research Centre, Winnipeg, MB. R. M. Foster’s census of connected symmetric trivalent graphs, With a foreword by H. S. M. Coxeter, With a biographical preface by Seymour Schuster, With an introduction by I. Z. Bouwer, W. W. Chernoff, B. Monson and Z. Star, Edited and with a note by Bouwer.Google Scholar
Fronček, Dalibor, Rosa, Alexander, and Širáň, Jozef. 1996. The existence of selfcomplementary circulant graphs. European J. Combin., 17(7), 625628.Google Scholar
Frucht, Roberto. 1936/37. Die gruppe des Petersen’schen Graphen und der Kantensysteme der regularen Polyeder. Comment. Math. Helv., 9, 217223.Google Scholar
Frucht, Robert. 1952. A one-regular graph of degree three. Canadian J. Math., 4, 240247.Google Scholar
Frucht, Roberto. 1970. How to describe a graph. Ann. New York Acad. Sci., 175, 159167.Google Scholar
Frucht, Roberto, Graver, Jack E., and Watkins, Mark E. 1971. The groups of the generalized Petersen graphs. Proc. Cambridge Philos. Soc., 70, 211218.Google Scholar
Gallai, T. 1968. On directed paths and circuits. Pages 115–118 of: Theory of Graphs (Proc. Colloq., Tihany, 1966). Academic Press, New York.Google Scholar
GAP. 2019. GAP – Groups, Algorithms, and Programming, Version 4.10.2. The GAP Group. Website. www.gap-system.orgGoogle Scholar
Gardiner, A. 1973. Arc transitivity in graphs. Quart. J. Math. Oxford Ser. (2), 24, 399407.CrossRefGoogle Scholar
Gardiner, A. 1974. Arc transitivity in graphs. II. Quart. J. Math. Oxford Ser. (2), 25, 163167.Google Scholar
Gardiner, A. 1976. Arc transitivity in graphs. III. Quart. J. Math. Oxford Ser. (2), 27(107), 313323.Google Scholar
Ghaderpour, Ebrahim, and Morris, Dave Witte. 2011. Cayley graphs of order 27p are Hamiltonian. Int. J. Comb., Art. ID 206930, 16.Google Scholar
Ghaderpour, Ebrahim, and Morris, Dave Witte. 2012. Cayley graphs of order 30p are Hamiltonian. Discrete Math., 312(24), 36143625.Google Scholar
Ghaderpour, Ebrahim, and Morris, Dave Witte. 2014. Cayley graphs on nilpotent groups with cyclic commutator subgroup are Hamiltonian. Ars Math. Contemp., 7(1), 5572.Google Scholar
Giudici, Michael. 2003. Quasiprimitive groups with no fixed point free elements of prime order. J. London Math. Soc. (2), 67(1), 7384.Google Scholar
Giudici, Michael. 2007. New constructions of groups without semiregular subgroups. Comm. Algebra, 35(9), 27192730.Google Scholar
Giudici, Michael, and Smith, Murray R. 2010. A note on quotients of strongly regular graphs. Ars Math. Contemp., 3(2), 147150.Google Scholar
Giudici, Michael, and Verret, Gabriel. 2020. Arc-transitive graphs of valency twice a prime admit a semiregular automorphism. Ars Math. Contemp., 18(1), 179186.Google Scholar
Giudici, Michael, and Xu, Jing. 2007. All vertex-transitive locally-quasiprimitive graphs have a semiregular automorphism. J. Algebraic Combin., 25(2), 217232.Google Scholar
Giudici, Michael, Li, Cai Heng, Potočnik, Primož, and Praeger, Cheryl E. 2007. Homogeneous factorisations of complete multipartite graphs. Discrete Math., 307(3–5), 415431.Google Scholar
Giudici, Michael, Li, Cai Heng, Potočnik, Primož, and Praeger, Cheryl E. 2008. Homogeneous factorisations of graph products. Discrete Math., 308(16), 36523667.Google Scholar
Glover, Henry, and Marušič, Dragan. 2007. Hamiltonicity of cubic Cayley graphs. J. Eur. Math. Soc. (JEMS), 9(4), 775787.Google Scholar
Glover, H. H., and Yang, T. Y. 1996. A Hamilton cycle in the Cayley graph of the ‹2, p, 3› presentation of PSL2(p). Discrete Math., 160(1-3), 149163.Google Scholar
Glover, Henry H., Kutnar, Klavdija, and Marušič, Dragan. 2009. Hamiltonian cycles in cubic Cayley graphs: the ‹2, 4k, 3› case. J. Algebraic Combin., 30(4), 447475.Google Scholar
Glover, Henry H., Kutnar, Klavdija, Malnič, Aleksander, and Marušič, Dragan. 2012. Hamilton cycles in (2, odd, 3)-Cayley graphs. Proc. Lond. Math. Soc. (3), 104(6), 11711197.Google Scholar
Godsil, C. D. 1980. More odd graph theory. Discrete Math., 32(2), 205207.Google Scholar
Godsil, C. D. 1981a. GRRs for nonsolvable groups. Pages 221–239 of: Algebraic Methods in Graph Theory, Vol. I, II (Szeged, 1978). Colloq. Math. Soc. János Bolyai, vol. 25. North-Holland, Amsterdam.Google Scholar
Godsil, C. D. 1981b. On the full automorphism group of a graph. Combinatorica, 1(3), 243256.CrossRefGoogle Scholar
Godsil, C. D. 1983. On Cayley graph isomorphisms. Ars Combin., 15, 231246.Google Scholar
Godsil, Chris, and Royle, Gordon. 2001. Algebraic Graph Theory. Graduate Texts in Mathematics, vol. 207. Springer-Verlag, New York.Google Scholar
Goldschmidt, David M. 1980. Automorphisms of trivalent graphs. Ann. of Math. (2), 111(2), 377406.CrossRefGoogle Scholar
Gorenstein, Daniel. 1968. Finite Groups. Harper & Row Publishers, New York.Google Scholar
Graham, R. L., Grötschel, M., and Lovász, L. (eds). 1995. Handbook of Combinatorics. Vol. 1, 2. Elsevier Science B.V., Amsterdam; MIT Press, Cambridge, MA.Google Scholar
Gray, F. 1953. Pulse Code Communication. US Patent 2632058. Issued March 17, 1953.Google Scholar
Gross, Fletcher. 1987. Conjugacy of odd order Hall subgroups. Bull. London Math. Soc., 19(4), 311319.Google Scholar
Gross, Jonathan L., and Tucker, Thomas W. 1987. Topological Graph Theory. Wiley-Interscience Series in Discrete Mathematics and Optimization. John Wiley & Sons, Inc., New York. A Wiley-Interscience Publication.Google Scholar
Grünbaum, Branko. 2009. Configurations of Points and Lines. Graduate Studies in Mathematics, vol. 103. American Mathematical Society, Providence, RI.Google Scholar
Guralnick, Robert M. 1983. Subgroups of prime power index in a simple group. J. Algebra, 81(2), 304311.Google Scholar
Guy, Richard Kenneth (ed). 1970. Combinatorial structures and their applications. Proceedings of the Calgary International Conference on Combinatorial Structures and Their Applications Held at the University of Calgary, Calgary, Alberta, Canada, June, vol. 1969. Gordon and Breach Science Publishers, New York.Google Scholar
Han, Hua, and Lu, Zai Ping. 2013. Affine primitive groups and semisymmetric graphs. Electron. J. Combin., 20(2), P39.Google Scholar
Harary, Frank. 1959. On the group of the composition of two graphs. Duke Math. J., 26, 2934.Google Scholar
Hassani, Akbar, Iranmanesh, Mohammad A., and Praeger, Cheryl E. 1998. On vertex-imprimitive graphs of order a product of three distinct odd primes. J. Combin. Math. Combin. Comput., 28, 187213. Papers in honour of Anne Penfold Street.Google Scholar
Higman, D. G. 1967. Intersection matrices for finite permutation groups. J. Algebra, 6, 2242.Google Scholar
Hladnik, Milan, Marušič, Dragan, and Pisanski, Tomaž. 2002. Cyclic Haar graphs. Discrete Math., 244(1–3), 137152.Google Scholar
Holt, D. F. 1981. A graph which is edge transitive but not arc transitive. J. Graph Theory, 5(2), 201204.Google Scholar
Holt, Derek, and Royle, Gordon. 2020. A census of small transitive groups and vertex-transitive graphs. J. Symbolic Comput., 101, 5160.Google Scholar
Holton, D. 1982. Research problem 9. Discrete Math., 38(1), 125.Google Scholar
Holton, D. A., and Sheehan, J. 1993. The Petersen Graph. Australian Mathematical Society Lecture Series, vol. 7. Cambridge University Press, Cambridge.Google Scholar
Howard, Ben, Millson, John, Snowden, Andrew, and Vakil, Ravi. 2008. A description of the outer automorphism of S6, and the invariants of six points in projective space. J. Combin. Theory Ser. A, 115(7), 12961303.Google Scholar
Hua, Xiao-Hui, Feng, Yan-Quan, and Lee, Jaeun. 2011. Pentavalent symmetric graphs of order 2pq. Discrete Math., 311(20), 22592267.Google Scholar
Hujdurović, Ademir, Kutnar, Klavdija, and Marušič, Dragan. 2013. On prime-valent symmetric bicirculants and Cayley snarks. Pages 196–203 of: Geometric Science of Information. Lecture Notes in Comput. Sci., vol. 8085. Springer, Heidelberg.Google Scholar
Hujdurović, Ademir, Kutnar, Klavdija, and Marušič, Dragan. 2014. Half-arc-transitive group actions with a small number of alternets. J. Combin. Theory Ser. A, 124, 114129.Google Scholar
Hujdurović, Ademir, Kutnar, Klavdija, and Marušič, Dragan. 2015. Vertex-transitive generalized Cayley graphs which are not Cayley graphs. European J. Combin., 46, 4550.Google Scholar
Hujdurović, Ademir, Kutnar, Klavdija, and Marušič, Dragan. 2016. Odd automorphisms in vertex-transitive graphs. Ars Math. Contemp., 10(2), 427437.Google Scholar
Imrich, Wilfried, Klavžar, Sandi, and Rall, Douglas F. 2008. Topics in Graph Theory. Wellesley, MA: A K Peters Ltd. Graphs and their Cartesian product.Google Scholar
Isaacs, I. Martin. 2008. Finite Group Theory. Graduate Studies in Mathematics, vol. 92. American Mathematical Society, Providence, RI.Google Scholar
Ivanov, A. A., and Iofinova, M. E. 1985. Biprimitive cubic graphs. Pages 123–134 of: Investigations in the Algebraic Theory of Combinatorial Objects (Russian). Vsesoyuz. Nauchno-Issled. Inst. Sistem. Issled., Moscow.Google Scholar
Jackson, Bill. 1980. Hamilton cycles in regular 2-connected graphs. J. Combin. Theory Ser. B, 29(1), 2746.Google Scholar
Jaeger, F. 1974. On vertex-induced forests in cubic graphs. Pages 501–512. Congressus Numerantium, No. X of: Proceedings of the Fifth Southeastern Conference on Combinatorics, Graph Theory and Computing (Florida Atlantic Univ., Boca Raton, FL, 1974).Google Scholar
Jajcay, Robert, and Li, Cai Heng. 2001. Constructions of self-complementary circulants with no multiplicative isomorphisms. European J. Combin., 22(8), 10931100.Google Scholar
Jajcay, Robert, Miklavič, Štefko, Šparl, Primož, and Vasiljević, Gorazd. 2019. On certain edge-transitive bicirculants. Electron. J. Combin., 26(2), P2.6.Google Scholar
Janusz, Gerald, and Rotman, Joseph. 1982. Outer automorphisms of S6. Amer. Math. Monthly, 89(6), 407410.Google Scholar
Jones, Gareth A. 1979. Abelian subgroups of simply primitive groups of degree p3, where p is prime. Quart. J. Math. Oxford Ser. (2), 30(117), 5376.Google Scholar
Jones, Gareth A. 2002. Cyclic regular subgroups of primitive permutation groups. J. Group Theory, 5(4), 403407.Google Scholar
Jones, Gareth A., and Jajcay, Robert. 2016. Cayley properties of merged Johnson graphs. J. Algebraic Combin., 44(4), 10471067.Google Scholar
Jones, Gareth A., and Singerman, David. 1978. Theory of maps on orientable surfaces. Proc. London Math. Soc. (3), 37(2), 273307.Google Scholar
Jordan, C. 1872. Recherches sur les substitutions. J. Math. Pures Appl., 17, 351367.Google Scholar
Joseph, Anne. 1995. The isomorphism problem for Cayley digraphs on groups of prime-squared order. Discrete Math., 141(1–3), 173183.Google Scholar
Kaloujnine, Léo. 1948. La structure des p-groupes de Sylow des groupes symétriques finis. Ann. Sci. École Norm. Sup. (3), 65, 239276.Google Scholar
Kalužnin, L. A., and Klin, M. H. 1976. Some numerical invariants of permutation groups. Latviĭsk. Mat. Ežegodnik, 8199, 222.Google Scholar
Kantor, William M. 1985. Classification of 2-transitive symmetric designs. Graphs Combin., 1(2), 165166.Google Scholar
Katona, G. O. H. 1972. A simple proof of the Erdős–Chao Ko–Rado theorem. J. Combin. Theory Ser. B, 13, 183184.Google Scholar
Keating, Kevin, and Witte, David. 1985. On Hamilton cycles in Cayley graphs in groups with cyclic commutator subgroup. Pages 89–102 of: Cycles in Graphs (Burnaby, B.C., 1982). North-Holland Math. Stud., vol. 115. North-Holland, Amsterdam.Google Scholar
Kleidman, Peter, and Liebeck, Martin. 1990. The Subgroup Structure of the Finite Classical Groups. London Mathematical Society Lecture Note Series, vol. 129. Cambridge University Press, Cambridge.Google Scholar
Klin, M. H., and Pöschel, R. 1981. The König problem, the isomorphism problem for cyclic graphs and the method of Schur rings. Pages 405–434 of: Algebraic methods in graph theory, Vol. I, II (Szeged, 1978). Colloq. Math. Soc. János Bolyai, vol. 25. North-Holland, Amsterdam.Google Scholar
Klin, Mikhail, Lauri, Josef, and Ziv-Av, Matan. 2012. Links between two semisymmetric graphs on 112 vertices via association schemes. J. Symbolic Comput., 47(10), 11751191.Google Scholar
Kneser, M. 1955. Aufgabe 300. Jber. Deutsch. Math.-Verein, 58, 27.Google Scholar
Koike, Hiroki, and Kovács, István. 2014. Isomorphic tetravalent cyclic Haar graphs. Ars Math. Contemp., 7(1), 215235.CrossRefGoogle Scholar
Koike, Hiroki, Kovács, István, Marušič, Dragan, and Muzychuk, Mikhail. 2019. Cyclic groups are CI-groups for balanced configurations. Des. Codes Cryptogr., 87(6), 12271235.Google Scholar
Kotlov, Andrew, and Lovász, László. 1996. The rank and size of graphs. J. Graph Theory, 23(2), 185189.Google Scholar
Kovács, István. 2004. Classifying arc-transitive circulants. J. Algebraic Combin., 20(3), 353358.Google Scholar
Kovács, István, and Ryabov, Grigory. 2022. The group is a DCI-group. Discrete Math. 345(3), Paper No. 112705, 15.Google Scholar
Kovács, István, and Servatius, Mary. 2012. On Cayley digraphs on nonisomorphic 2-groups. J. Graph Theory, 70(4), 435448.Google Scholar
Kovács, István, Kutnar, Klavdija, and Marušič, Dragan. 2010. Classification of edgetransitive rose window graphs. J. Graph Theory, 65(3), 216231.Google Scholar
Kovács, István, Marušič, Dragan, and Muzychuk, Mikhail E. 2011. On dihedrants admitting arc-regular group actions. J. Algebraic Combin., 33(3), 409426.Google Scholar
Kovács, István, Marušič, Dragan, and Muzychuk, Mikhail. 2013. On G-arc-regular dihedrants and regular dihedral maps. J. Algebraic Combin., 38(2), 437455.Google Scholar
Kowalewski, A. 1917. W.R. Hamilton’s Dodeaederaufgabe als Buntordnungsproblem. Sitzungsber. Akad. Wiss. Wien (Abt. IIa), 126, 6790, 9631007.Google Scholar
Krasner, Marc, and Kaloujnine, Léo. 1951. Produit complet des groupes de permutations et problème de groupes. II. Acta Sci. Math. (Szeged), 14, 3966.Google Scholar
Kriloff, Cathy, and Lay, Terry. 2014. Hamiltonian cycles in Cayley graphs of imprimitive complex reflection groups. Discrete Math., 326, 5060.Google Scholar
Krivelevich, Michael, and Sudakov, Benny. 2003. Sparse pseudo-random graphs are Hamiltonian. J. Graph Theory, 42(1), 1733.Google Scholar
Kutnar, Klavdija, and Marušič, Dragan. 2008a. Hamiltonicity of vertex-transitive graphs of order 4 p. European J. Combin., 29(2), 423438.Google Scholar
Kutnar, Klavdija, and Marušič, Dragan. 2008b. Recent trends and future directions in vertex-transitive graphs. Ars Math. Contemp., 1(2), 112125.Google Scholar
Kutnar, Klavdija, and Marušič, Dragan. 2009a. A complete classification of cubic symmetric graphs of girth 6. J. Combin. Theory Ser. B, 99(1), 162184.Google Scholar
Kutnar, Klavdija, and Marušič, Dragan. 2009b. Hamilton cycles and paths in vertextransitive graphs – current directions. Discrete Math., 309(17), 54915500.Google Scholar
Kutnar, Klavdija, and Marušič, Dragan. 2019. Odd extensions of transitive groups via symmetric graphs – the cubic case. J. Combin. Theory Ser. B, 136, 170192.Google Scholar
Kutnar, Klavdija, and Šparl, Primož. 2009. Hamilton paths and cycles in vertex-transitive graphs of order 6p. Discrete Math., 309(17), 54445460.Google Scholar
Kutnar, Klavdija, and Šparl, Primož. 2010. Distance-transitive graphs admit semiregular automorphisms. European J. Combin., 31(1), 2528.Google Scholar
Kutnar, Klavdija, Marušič, Dragan, Miklavič, Štefko, and Šparl, Primož. 2009. Strongly regular tri-Cayley graphs. European J. Combin., 30(4), 822832.Google Scholar
Kutnar, Klavdija, Marušič, Dragan, and Šparl, Primož. 2010. An infinite family of half-arc-transitive graphs with universal reachability relation. European J. Combin., 31(7), 17251734.Google Scholar
Kutnar, K., Marušič, D., Morris, D. W., Morris, J., and Šparl, P. 2012a. Hamiltonian cycles in Cayley graphs whose order has few prime factors. Ars Math. Contemp., 5(1), 2771.Google Scholar
Kutnar, Klavdija, Marušič, Dragan, and Zhang, Cui. 2012b. Hamilton paths in vertex-transitive graphs of order 10p. European J. Combin., 33(6), 10431077.Google Scholar
Lambossy, P. 1931. Sur une manière de différencier les fonctions cycliques d’une forme donnée. Comment. Math. Helv., 3(1), 69102.Google Scholar
Leung, Ka Hin, and Man, Shing Hing. 1996. On Schur rings over cyclic groups. II. J. Algebra, 183(2), 273285.Google Scholar
Leung, Ka Hin, and Man, Shing Hing. 1998. On Schur rings over cyclic groups. Israel J. Math., 106, 251267.Google Scholar
Levi, F. W. 1942. Finite Geometrical Systems. University of Calcutta, Calcutta.Google Scholar
Li, Cai Heng. 1998. On isomorphisms of connected Cayley graphs. Discrete Math., 178(1–3), 109122.Google Scholar
Li, Cai Heng. 1999. Finite CI-groups are soluble. Bull. London Math. Soc., 31(4), 419423.Google Scholar
Li, Cai Heng. 2002. On isomorphisms of finite Cayley graphs – a survey. Discrete Math., 256(1–2), 301334.Google Scholar
Li, Cai Heng. 2003. The finite primitive permutation groups containing an abelian regular subgroup. Proc. London Math. Soc. (3), 87(3), 725747.Google Scholar
Li, Cai Heng. 2005. Permutation groups with a cyclic regular subgroup and arc transitive circulants. J. Algebraic Combin., 21(2), 131136.Google Scholar
Li, Cai Heng, and Praeger, Cheryl E. 2002. Constructing homogeneous factorisations of complete graphs and digraphs. Graphs Combin., 18(4), 757761.Google Scholar
Li, Cai Heng, and Seress, Ákos. 2003. The primitive permutation groups of squarefree degree. Bull. London Math. Soc., 35(5), 635644.Google Scholar
Li, Cai Heng, and Seress, Ákos. 2005. On vertex-transitive non-Cayley graphs of square-free order. Des. Codes Cryptogr., 34(2–3), 265281.Google Scholar
Li, Cai Heng, and Sim, Hyo-Seob. 2001. On half-transitive metacirculant graphs of prime-power order. J. Combin. Theory Ser. B, 81(1), 4557.Google Scholar
Li, Cai Heng, Lu, Zai Ping, and Marušič, Dragan. 2004. On primitive permutation groups with small suborbits and their orbital graphs. J. Algebra, 279(2), 749770.CrossRefGoogle Scholar
Li, Cai Heng, Lu, Zai Ping, and Pálfy, P. P. 2007. Further restrictions on the structure of finite CI-groups. J. Algebraic Combin., 26(2), 161181.Google Scholar
Li, Cai Heng, Lim, Tian Khoon, and Praeger, Cheryl E. 2009. Homogeneous factorisations of complete graphs with edge-transitive factors. J. Algebraic Combin., 29(1), 107132.Google Scholar
Li, Cai Heng, Song, Shu Jiao, and Wang, Dian Jun. 2013. A characterization of metacirculants. J. Combin. Theory Ser. A, 120(1), 3948.Google Scholar
Li, Cai Heng, Sun, Shaohui, and Xu, Jing. 2014. Self-complementary circulants of prime-power order. SIAM J. Discrete Math., 28(1), 817.Google Scholar
Liebeck, Martin W., and Saxl, Jan. 1985a. Primitive permutation groups containing an element of large prime order. J. London Math. Soc. (2), 31(2), 237249.Google Scholar
Liebeck, Martin W., and Saxl, Jan. 1985b. The primitive permutation groups of odd degree. J. London Math. Soc. (2), 31(2), 250264.Google Scholar
Liebeck, Martin W., and Seitz, Gary M. 1990. Maximal subgroups of exceptional groups of Lie type, finite and algebraic. Geom. Dedicata, 35(1–3), 353387.Google Scholar
Liebeck, Martin W., and Seitz, Gary M. 1999. On finite subgroups of exceptional algebraic groups. J. Reine Angew. Math., 515, 2572.Google Scholar
Liebeck, Martin W., and Seitz, Gary M. 2004. The maximal subgroups of positive dimension in exceptional algebraic groups. Mem. Amer. Math. Soc., 169(802), vi+227.Google Scholar
Liebeck, Martin W., and Seitz, Gary M. 2005. Maximal subgroups of large rank in exceptional groups of Lie type. J. London Math. Soc. (2), 71(2), 345361.Google Scholar
Liebeck, Martin W., Praeger, Cheryl E., and Saxl, Jan. 1987. A classification of the maximal subgroups of the finite alternating and symmetric groups. J. Algebra, 111(2), 365383.Google Scholar
Liebeck, Martin W., Praeger, Cheryl E., and Saxl, Jan. 1988. On the O’Nan-Scott theorem for finite primitive permutation groups. J. Austral. Math. Soc. Ser. A, 44(3), 389396.Google Scholar
Liebeck, Martin W., Praeger, Cheryl E., and Saxl, Jan. 2010. Regular subgroups of primitive permutation groups. Mem. Amer. Math. Soc., 203(952), vi+74.Google Scholar
Lipschutz, Seymour, and Xu, Ming-Yao. 2002. Note on infinite families of trivalent semisymmetric graphs. European J. Combin., 23(6), 707711.Google Scholar
Liskovets, Valery, and Pöschel, Reinhard. 2000. Non-Cayley-isomorphic self-complementary circulant graphs. J. Graph Theory, 34(2), 128141.Google Scholar
Livingstone, Donald, and Wagner, Ascher. 1965. Transitivity of finite permutation groups on unordered sets. Math. Z., 90, 393403.Google Scholar
Lorimer, Peter. 1984. Vertex-transitive graphs: symmetric graphs of prime valency. J. Graph Theory, 8(1), 5568.Google Scholar
Lovász, L. 1978. Kneser’s conjecture, chromatic number, and homotopy. J. Combin. Theory Ser. A, 25(3), 319324.Google Scholar
Lovász, L. 1979. Combinatorial Problems and Exercises. North-Holland Publishing Co., Amsterdam-New York.Google Scholar
Lovrečič Saražin, Marko. 1997. A note on the generalized Petersen graphs that are also Cayley graphs. J. Combin. Theory Ser. B, 69(2), 226229.Google Scholar
Luks, Eugene M. 1982. Isomorphism of graphs of bounded valence can be tested in polynomial time. J. Comput. System Sci., 25(1), 4265.Google Scholar
Malnič, Aleksander, and Marušič, Dragan. 2002. Constructing -arc-transitive graphs of valency 4 and vertex stabilizer Z2 × Z2. Discrete Math., 245(1–3), 203216.Google Scholar
Malnič, Aleksander, and Marušič, Dragan. 2002b. Constructing -arc-transitive graphs of valency 4 and vertex stabilizer Z2 × Z2. Discrete Math., 245(1-3), 203216.Google Scholar
Malnič, Aleksander, Nedela, Roman, and Škoviera, Martin. 2000. Lifting graph automorphisms by voltage assignments. European J. Combin., 21(7), 927947.Google Scholar
Malnič, Aleksander, Marušič, Dragan, and Šparl, Primož. 2007a. On strongly regular bicirculants. European J. Combin., 28(3), 891900.Google Scholar
Malnič, Aleksander, Marušič, Dragan, Miklavič, Štefko, and Potočnik, Primož. 2007b. Semisymmetric elementary abelian covers of the Möbius–Kantor graph. Discrete Math., 307(17–18), 21562175.Google Scholar
Marušič, D. 1985.Vertex transitive graphs and digraphs of order pk. Pages 115–128 of: Cycles in Graphs (Burnaby, BC, 1982). North-Holland Math. Stud., vol. 115. Amsterdam: North-Holland.Google Scholar
Marušič, Dragan. 1981a. On vertex symmetric digraphs. Discrete Math., 36(1), 6981.Google Scholar
Marušič, Dragan. 1981b. On Vertex Symmetric Digraphs. PhD thesis, University of Reading.Google Scholar
Marušič, Dragan. 1983. Cayley properties of vertex symmetric graphs. Ars Combin., 16(B), 297302.Google Scholar
Marušič, Dragan. 1987. Hamiltonian cycles in vertex symmetric graphs of order 2p2. Discrete Math., 66(1–2), 169174.Google Scholar
Marušič, Dragan. 1988a. On vertex-transitive graphs of order qp. J. Combin. Math. Combin. Comput., 4, 97114.Google Scholar
Marušič, Dragan. 1988b. Strongly regular bicirculants and tricirculants. Ars Combin., 25(C), 1115. Eleventh British Combinatorial Conference (London, 1987).Google Scholar
Marušič, Dragan. 1992. Hamiltonicity of vertex-transitive pq-graphs. Pages 209–212 of: Fourth Czechoslovakian Symposium on Combinatorics, Graphs and Complexity (Prachatice, 1990). Ann. Discrete Math., vol. 51. North-Holland, Amsterdam.Google Scholar
Marušič, Dragan. 1998. Half-transitive group actions on finite graphs of valency 4. J. Combin. Theory Ser. B, 73(1), 4176.Google Scholar
Marušič, Dragan. 2000. Constructing cubic edge-but not vertex-transitive graphs. J. Graph Theory, 35(2), 152160.Google Scholar
Marušič, Dragan. 2003. On 2-arc-transitivity of Cayley graphs. J. Combin. Theory Ser. B, 87(1), 162196. Dedicated to Crispin Nash-Williams, St. J. A..Google Scholar
Marušič, Dragan. 2005. Quartic half-arc-transitive graphs with large vertex stabilizers. Discrete Math., 299(1–3), 180193.Google Scholar
Marušič, Dragan. 2018. Semiregular automorphisms in vertex-transitive graphs of order 3p2. Electron. J. Combin., 25(2), P2.25.Google Scholar
Marušič, Dragan, and Nedela, Roman. 2001a. On the point stabilizers of transitive groups with non-self-paired suborbits of length 2. J. Group Theory, 4(1), 1943.Google Scholar
Marušič, Dragan, and Nedela, Roman. 2001b. Partial line graph operator and half-arc-transitive group actions. Math. Slovaca, 51(3), 241257.Google Scholar
Marušič, Dragan, and Parsons, T. D. 1982. Hamiltonian paths in vertex-symmetric graphs of order 5p. Discrete Math., 42(2–3), 227242.Google Scholar
Marušič, Dragan, and Parsons, T. D. 1983. Hamiltonian paths in vertex-symmetric graphs of order 4p. Discrete Math., 43(1), 9196.Google Scholar
Marušič, Dragan, and Pisanski, Tomaž. 2000. The remarkable generalized Petersen graph G(8, 3). Math. Slovaca, 50(2), 117121.Google Scholar
Marušič, Dragan, and Praeger, Cheryl E. 1999. Tetravalent graphs admitting half-transitive group actions: alternating cycles. J. Combin. Theory Ser. B, 75(2), 188205.Google Scholar
Marušič, Dragan, and Scapellato, Raffaele. 1992a. Characterizing vertex-transitive pq-graphs with an imprimitive automorphism subgroup. J. Graph Theory, 16(4), 375387.Google Scholar
Marušič, Dragan, and Potočnik, Primož. 2001. Semisymmetry of generalized Folkman graphs. European J. Combin., 22(3), 333349.Google Scholar
Marušič, Dragan, and Potočnik, Primož. 2002. Bridging semisymmetric and half-arc-transitive actions on graphs. European J. Combin., 23(6), 719732.Google Scholar
Marušič, Dragan, and Scapellato, Raffaele. 1992b. A class of non-Cayley vertex-transitive graphs associated with PSL(2, p). Discrete Math., 109(1–3), 161170. Algebraic graph theory (Leibnitz, 1989).Google Scholar
Marušič, Dragan, and Scapellato, Raffaele. 1993. Imprimitive representations of SL(2, 2k). J. Combin. Theory Ser. B, 58(1), 4657.Google Scholar
Marušič, Dragan, and Scapellato, Raffaele. 1994a. A class of graphs arising from the action of PSL(2, q2) on cosets of PGL(2, q). Discrete Math., 134(1–3), 99110. Algebraic and topological methods in graph theory.Google Scholar
Marušič, D., and Scapellato, R. 1994b. Classifying vertex-transitive graphs whose order is a product of two primes. Combinatorica, 14(2), 187201.Google Scholar
Marušič, Dragan, and Scapellato, Raffaele. 1994c. Permutation groups with conjugacy complete stabilizers. Discrete Math., 134(1–3), 9398.Google Scholar
Marušič, Dragan, and Scapellato, Raffaele. 1998. Permutation groups, vertex-transitive digraphs and semiregular automorphisms. European J. Combin., 19(6), 707712.Google Scholar
Marušič, Dragan, and Šparl, Primož. 2008. On quartic half-arc-transitive metacirculants. J. Algebraic Combin., 28(3), 365395.Google Scholar
Marušič, Dragan, and Xu, Ming-Yao. 1997. A -transitive graph of valency 4 with a nonsolvable group of automorphisms. J. Graph Theory, 25(2), 133138.Google Scholar
Marušič, Dragan, Scapellato, Raffaele, and Zagaglia Salvi, Norma. 1992. Generalized Cayley graphs. Discrete Math., 102(3), 279285.Google Scholar
McKay, Brendan D., and Praeger, Cheryl E. 1994. Vertex-transitive graphs which are not Cayley graphs. I. J. Austral. Math. Soc. Ser. A, 56(1), 5363.Google Scholar
McKay, Brendan D., and Praeger, Cheryl E. 1996. Vertex-transitive graphs that are not Cayley graphs. II. J. Graph Theory, 22(4), 321334.Google Scholar
McKay, Brendan D., and Royle, Gordon F. 1990. The transitive graphs with at most 26 vertices. Ars Combin., 30, 161176.Google Scholar
Miklavič, Štefko, Potočnik, Primož, and Wilson, Steve. 2007a. Consistent cycles in graphs and digraphs. Graphs Combin., 23(2), 205216.Google Scholar
Miklavič, Štefko, Potočnik, Primož, and Wilson, Steve. 2007b. Overlap in consistent cycles. J. Graph Theory, 55(1), 5571.Google Scholar
Miller, G. A. 1903. A fundamental theorem with respect to transitive substitution groups. Bull. Amer. Math. Soc., 9(10), 543544.Google Scholar
Miller, G. A. 1915. Limits of the degree of transitivity of substitution groups. Bull. Amer. Math. Soc., 22(2), 6871.Google Scholar
Miller, Robert C. 1971. The trivalent symmetric graphs of girth at most six. J. Combin. Theory Ser. B, 10, 163182.Google Scholar
Mohar, Bojan. 1992. A domain monotonicity theorem for graphs and Hamiltonicity. Discrete Appl. Math., 36(2), 169177.Google Scholar
Monson, Barry, Pisanski, Tomaž, Schulte, Egon, and Weiss, Asia Ivić. 2007. Semisymmetric graphs from polytopes. J. Combin. Theory Ser. A, 114(3), 421435.Google Scholar
Morris, Dave Witte. 2016. Infinitely many nonsolvable groups whose Cayley graphs are hamiltonian. J. Algebra Comb. Discrete Struct. Appl., 3(1), 1330.Google Scholar
Morris, Dave Witte. 2018. Cayley graphs on groups with commutator subgroup of order 2p are hamiltonian. The Art of Discrete and Applied Math., 1(1), #P04.Google Scholar
Morris, Joy. 1999. Isomorphic Cayley graphs on nonisomorphic groups. J. Graph Theory, 31(4), 345362.Google Scholar
Morris, Joy, and Spiga, Pablo. 2018a. Asymptotic enumeration of Cayley digraphs. Israel J., Math., 242(1), 401459.Google Scholar
Morris, Joy, and Spiga, Pablo. 2018b. Classification of finite groups that admit an oriented regular representation. Bull. Lond. Math. Soc., 50(5), 811831.Google Scholar
Morris, Joy, and Tymburski, Josh. 2018. Most rigid representations and Cayley index. Art Discrete Appl. Math., 1(1).Google Scholar
Morris, Joy, Spiga, Pablo, and Verret, Gabriel. 2015. Automorphisms of Cayley graphs on generalised dicyclic groups. European J. Combin., 43, 6881.Google Scholar
Müller, Peter. 2013. Permutation groups with a cyclic two-orbits subgroup and monodromy groups of Laurent polynomials. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), 12(2), 369438.Google Scholar
Mütze, Torsten, Nummenpalo, Jerri, and Walczak, Bartosz. 2018. Sparse Kneser graphs are Hamiltonian. Pages 912–919 of: STOC’18 – Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing. ACM, New York.Google Scholar
Muzychuk, Mikhail. 1995. Ádám’s conjecture is true in the square-free case. J. Combin. Theory Ser. A, 72(1), 118134.Google Scholar
Muzychuk, Mikhail. 1997. On Ádám’s conjecture for circulant graphs. Discrete Math., 176(1–3), 285298.Google Scholar
Muzychuk, Mikhail. 1999. On the isomorphism problem for cyclic combinatorial objects. Discrete Math., 197/198, 589606. 16th British Combinatorial Conference (London, 1997).Google Scholar
Muzychuk, M. 2003. An elementary abelian group of large rank is not a CI-group. Discrete Math., 264(1–3), 167185. The 2000 Com2 MaC Conference on Association Schemes, Codes and Designs (Pohang).Google Scholar
Muzychuk, M. 2004. A solution of the isomorphism problem for circulant graphs. Proc. London Math. Soc. (3), 88(1), 141.Google Scholar
Muzychuk, Mikhail. 2015. A solution of an equivalence problem for semisimple cyclic codes. Pages 327–334 of: Topics in Finite Fields. Contemp. Math., vol. 632. Amer. Math. Soc., Providence, RI.Google Scholar
Muzychuk, Mikhail, and Ponomarenko, Ilia. 2009. Schur rings. European J. Combin., 30(6), 15261539.Google Scholar
Nedela, Roman, and Škoviera, Martin. 1995a. Which generalized Petersen graphs are Cayley graphs? J. Graph Theory, 19(1), 111.Google Scholar
Nedela, Roman, and Škoviera, Martin. 1995b. Atoms of cyclic connectivity in cubic graphs. Math. Slovaca, 45(5), 481499.Google Scholar
Negami, S. 1985. Uniqueness and Faithfulness of Embeddings of Graphs into Surfaces. PhD thesis, Tokyo Inst. of Technology.Google Scholar
Neumann, Peter M. 1977. Finite permutation groups, edge-coloured graphs and matrices. Pages 82–118 of: Topics in Group Theory and Computation (Proc. Summer School, University College, Galway, 1973).Google Scholar
Neumann, Peter M. 2009. Primitive permutation groups and their section-regular partitions. Michigan Math. J., 58(1), 309322.Google Scholar
Nowitz, Lewis A. 1968. On the non-existence of graphs with transitive generalized dicyclic groups. J. Combin. Theory, 4, 4951.Google Scholar
Nowitz, Lewis A. 1992. A non-Cayley-invariant Cayley graph of the elementary abelian group of order 64. Discrete Math., 110(1–3), 223228.Google Scholar
Ore, Oystein. 1962. Theory of Graphs. American Mathematical Society Colloquium Publications, Vol. XXXVIII. American Mathematical Society, Providence, RI.Google Scholar
Pak, Igor, and Radoičić, Radoš. 2009. Hamiltonian paths in Cayley graphs. Discrete Math., 309(17), 55015508.Google Scholar
Pálfy, P. P. 1987. Isomorphism problem for relational structures with a cyclic automorphism. European J. Combin., 8(1), 3543.Google Scholar
Passman, Donald. 1968. Permutation Groups. W. A. Benjamin, Inc., New York-Amsterdam.Google Scholar
Payan, C., and Sakarovitch, M. 1975. Ensembles cycliquement stables et graphes cubiques. Cahiers Centre Études Recherche Opér., 17(2–4), 319343.Google Scholar
Pisanski, Tomaž. 2007. A classification of cubic bicirculants. Discrete Math., 307(3–5), 567578.Google Scholar
Pisanski, Tomaž, and Servatius, Brigitte. 2013. Configurations From a Graphical Viewpoint. Birkhäuser Advanced Texts: Basler Lehrbücher. [Birkhäuser Advanced Texts: Basel Textbooks]. Birkhäuser/Springer, New York.Google Scholar
Ponomarenko, I. N. 2005. Determination of the automorphism group of a circulant association scheme in polynomial time. Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI), 321 (Vopr. Teor. Predst. Algebr. i Grupp. 12), 251267, 301; English translation in: J. Math. Sci. (2006) 136(3), 3972–3979.Google Scholar
Potočnik, Primož, and Šajna, Mateja. 2006. On almost self-complementary graphs. Discrete Math., 306(1), 107123.Google Scholar
Potočnik, Primož, and Šajna, Mateja. 2007. Self-complementary two-graphs and almost self-complementary double covers. European J. Combin., 28(6), 15611574.Google Scholar
Potočnik, Primož, and Šajna, Mateja. 2009. Vertex-transitive self-complementary uniform hypergraphs. European J. Combin., 30(1), 327337.Google Scholar
Potočnik, Primož, and Wilson, Steve. 2016. Linking rings structures and semisymmetric graphs: Cayley constructions. European J. Combin., 51, 8498.Google Scholar
Potočnik, Primož, Spiga, Pablo, and Verret, Gabriel. 2012. On graph-restrictive permutation groups. J. Combin. Theory Ser. B, 102(3), 820831.Google Scholar
Potočnik, Primož, Spiga, Pablo, and Verret, Gabriel. 2013. Cubic vertex-transitive graphs on up to 1280 vertices. J. Symbolic Comput., 50, 465477.Google Scholar
Potočnik, Primož, Spiga, Pablo, and Verret, Gabriel. 2014. On the order of arc-stabilisers in arc-transitive graphs with prescribed local group. Trans. Amer. Math. Soc., 366(7), 37293745.Google Scholar
Potočnik, Primož, Spiga, Pablo, and Verret, Gabriel. 2015. A census of 4-valent half-arc-transitive graphs and arc-transitive digraphs of valence two. Ars Math. Contemp., 8(1), 133148.Google Scholar
Praeger, Cheryl E. 1985. Imprimitive symmetric graphs. Ars Combin., 19(A), 149163.Google Scholar
Praeger, Cheryl E. 1993. An O’Nan–Scott theorem for finite quasiprimitive permutation groups and an application to 2-arc transitive graphs. J. London Math. Soc. (2), 47(2), 227239.Google Scholar
Praeger, Cheryl E., and Xu, Ming Yao. 1993. Vertex-primitive graphs of order a product of two distinct primes. Vertex-primitive graphs of order a product of two distinct primes, 59(2), 245266.Google Scholar
Praeger, Cheryl, Li, Cai Heng, and Stringer, Linda. 2009. Common circulant homo-geneous factorisations of the complete digraph. Discrete Math., 309(10), 30063012.Google Scholar
Praeger, Cheryl E., Spiga, Pablo, and Verret, Gabriel. 2012. Bounding the size of a vertex-stabiliser in a finite vertex-transitive graph. J. Combin. Theory Ser. B, 102(3), 797819.Google Scholar
Praeger, Cheryl E., Wang, Ru Ji, and Xu, Ming Yao. 1993. Symmetric graphs of order a product of two distinct primes. J. Combin. Theory Ser. B, 58(2), 299318.Google Scholar
Quirin, William L. 1971. Primitive permutation groups with small orbitals. Math. Z., 122, 267274.Google Scholar
Ramos Rivera, Alejandra, and Šparl, Primož. 2017. The classification of half-arc-transitive generalizations of Bouwer graphs. European J. Combin., 64, 88112.Google Scholar
Ramos Rivera, Alejandra, and Šparl, Primož. 2019. New structural results on tetravalent half-arc-transitive graphs. J. Combin. Theory Ser. B, 135, 256278.Google Scholar
Ramras, Mark, and Donovan, Elizabeth. 2011. The automorphism group of a Johnson graph. Siam J. Discrete Math., 25, 267270.Google Scholar
Rapaport-Strasser, Elvira. 1959. Cayley color groups and Hamilton lines. Scripta Math., 24, 5158.Google Scholar
Royle, Gordon F. 2008. A normal non-Cayley-invariant graph for the elementary abelian group of order 64. J. Aust. Math. Soc., 85(3), 347351.Google Scholar
Ryabov, Grigory. 2020. The Cayley isomorphism property for the group . Ars Math. Contemp., 19(2), 277295.Google Scholar
Ryabov, Grigory. 2021. The Cayley isomorphism property for the group . Comm. Algebra 49(4), 17881804.Google Scholar
Sabidussi, Gert. 1958. On a class of fixed-point-free graphs. Proc. Amer. Math. Soc., 9, 800804.Google Scholar
Sabidussi, Gert. 1959. The composition of graphs. Duke Math. J., 26, 693696.Google Scholar
Sabidussi, Gert. 1964. Vertex-transitive graphs. Monatsh. Math., 68, 426438.Google Scholar
Sachs, Horst. 1962. Über selbstkomplementäre Graphen. Publ. Math. Debrecen, 9, 270288.Google Scholar
Schur, Issai. 1933. Zur Theorie der einfach transitiven Permutationsgruppen. S. B. Preuss. Akad. Wiss., Phys.-Math. KI, 70, 598623.Google Scholar
Scott, Leonard L. 1972. On permutation groups of degree 2 p. Math. Z., 126, 227229.Google Scholar
Scott, W. R. 1987. Group Theory. Second ed. Dover Publications Inc., New York.Google Scholar
Seress, Ákos. 1998. On vertex-transitive, non-Cayley graphs of order pqr. Discrete Math., 182(1–3), 279292.Google Scholar
Sims, Charles C. 1968. Graphs and finite permutation groups. II. Math. Z., 103, 276281.Google Scholar
Sjerve, Denis, and Cherkassoff, Michael. 1994. On groups generated by three involutions, two of which commute. Pages 169–185 of: The Hilton Symposium 1993 (Montreal, PQ). CRM Proc. Lecture Notes, vol. 6. Amer. Math. Soc., Providence, RI.Google Scholar
Smith, D. H. 1971. Primitive and imprimitive graphs. Quart. J. Math. Oxford Ser. (2), 22, 551557.Google Scholar
Somlai, Gábor. 2011. Elementary abelian p-groups of rank 2p + 3 are not CI-groups. J. Algebraic Combin., 34(3), 323335.Google Scholar
Somlai, Gábor. 2015. The Cayley isomorphism property for groups of order 8p. Ars Math. Contemp., 8(2), 433444.Google Scholar
Song, Shu Jiao, Li, Cai Heng, and Zhang, Hua. 2014. Finite permutation groups with a regular dihedral subgroup, and edge-transitive dihedrants. J. Algebra, 399, 948959.Google Scholar
Šparl, Primož. 2008. A classification of tightly attached half-arc-transitive graphs of valency 4. J. Combin. Theory Ser. B, 98(5), 10761108.Google Scholar
Spiga, Pablo. 2007. Elementary abelian p-groups of rank greater than or equal to 4p − 2 are not CI-groups. J. Algebraic Combin., 26(3), 343355.Google Scholar
Spiga, Pablo. 2018. On the existence of Frobenius digraphical representations. Electron. J. Combin., 25(2), P2.6.Google Scholar
Spiga, Pablo. 2021. On the equivalence between a conjecture of Babai–Godsil and a conjecture of Xu concerning the enumeration of Cayley graphs. Art Discrete Appl. Math., 4(1), P1.10.Google Scholar
Steimle, Alice, and Staton, William. 2009. The isomorphism classes of the generalized Petersen graphs. Discrete Math., 309(1), 231237.Google Scholar
Suprunenko, D. A. 1985. Self-complementary graphs. Kibernetika (Kiev), i, 16, 24, 133.Google Scholar
Thomassen, Carsten. 1991. Tilings of the torus and the Klein bottle and vertex-transitive graphs on a fixed surface. Trans. Amer. Math. Soc., 323(2), 605635.Google Scholar
Trofimov, V. I. 1990. Vertex stabilizers of graphs with projective suborbits. Dokl. Akad. Nauk SSSR, 315(3), 544546.Google Scholar
Trofimov, V. I. 1991. Graphs with projective suborbits. Izv. Akad. Nauk SSSR Ser. Mat., 55(4), 890916.Google Scholar
Turner, James. 1967. Point-symmetric graphs with a prime number of points. J. Combin. Theory, 3, 136145.Google Scholar
Tutte, W. T. 1947. A family of cubical graphs. Proc. Cambridge Philos. Soc., 43, 459474.Google Scholar
Tutte, W. T. 1959. On the symmetry of cubic graphs. Canad. J. Math., 11, 621624.Google Scholar
Tutte, W. T. 1960. A non-Hamiltonian graph. Canad. Math. Bull., 3, 15.Google Scholar
Tutte, W. T. 1966. Connectivity in graphs. Mathematical Expositions, No. 15. Toronto, Ont.: University of Toronto Press.Google Scholar
Tutte, W. T. 1998. Graph Theory as I Have Known It. Oxford Lecture Series in Mathematics and its Applications, vol. 11. The Clarendon Press, Oxford University Press, New York.Google Scholar
Tyshkevich, R. I., and Tan, Ngo Dak. 1987. A generalization of Babai’s lemma on Cayley graphs. Vestsĭ Akad. Navuk BSSR Ser. Fĭz.-Mat. Navuk, 2932, 124.Google Scholar
van den Heuvel, J. 1995. Hamilton cycles and eigenvalues of graphs. Linear Algebra Appl., 226/228, 723730.Google Scholar
Verret, Gabriel. 2009. On the order of arc-stabilizers in arc-transitive graphs. Bull. Aust. Math. Soc., 80(3), 498505.Google Scholar
Verret, Gabriel. 2015. Arc-transitive graphs of valency 8 have a semiregular automorphism. Ars Math. Contemp., 8(1), 2934.Google Scholar
Walther, Hansjoachim. 1969. Über die Nichtexistenz eines Knotenpunktes, durch den alle längsten Wege eines Graphen gehen. J. Combin. Theory, 6, 16.Google Scholar
Walther, Hansjoachim, and Voss, Heinz-Jürgen. 1974. Über Kreise in Graphen. VEB Deutscher Verlag der Wissenschaften, Berlin.Google Scholar
Wang, Chang Qun, and Chen, Tie Sheng. 2008. Semisymmetric cubic graphs as regular covers of K3,3. Acta Math. Sin. (Engl. Ser.), 24(3), 405416.Google Scholar
Wang, Changqun, Wang, Dianjun, and Xu, Mingyao. 1998. Normal Cayley graphs of finite groups. Sci. China Ser. A, 41(3), 242251.Google Scholar
Wang, Li, and Du, Shaofei. 2014. Semisymmetric graphs of order 2p3. European J. Combin., 36, 393405.Google Scholar
Wang, Li, Du, Shaofei, and Li, Xuewen. 2014. A class of semisymmetric graphs. Ars Math. Contemp., 7(1), 4053.Google Scholar
Wang, Ru Ji, and Xu, Ming Yao. 1993. A classification of symmetric graphs of order 3p. J. Combin. Theory Ser. B, 58(2), 197216.Google Scholar
Watkins, Mark E. 1969. A theorem on Tait colorings with an application to the generalized Petersen graphs. J. Combin. Theory, 6, 152164.Google Scholar
Watkins, Mark E. 1970. Connectivity of transitive graphs. J. Combin. Theory, 8, 2329.Google Scholar
Watkins, Mark E. 1990. Vertex-transitive graphs that are not Cayley graphs. Pages 243–256 of: Cycles and Rays (Montreal, PQ, 1987). NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., vol. 301. Kluwer Academic Publishers, Dordrecht.Google Scholar
Weiss, Richard. 1979. An application of p-factorization methods to symmetric graphs. Math. Proc. Cambridge Philos. Soc., 85(1), 4348.Google Scholar
Weiss, R. 1981a. s-transitive graphs. Pages 827–847 of: Algebraic Methods in Graph Theory, Vol. I, II (Szeged, 1978). Colloq. Math. Soc. János Bolyai, vol. 25. North-Holland, Amsterdam-New York.Google Scholar
Weiss, Richard. 1981b. The nonexistence of 8-transitive graphs. Combinatorica, 1(3), 309311.Google Scholar
Wielandt, Helmut. 1964. Finite Permutation Groups. Translated from the German by R. Bercov. Academic Press, New York.Google Scholar
Wielandt, H. 1969. Permutation Groups Through Invariant Relations and Invariant Functions. Lectures given at The Ohio State University, Columbus, Ohio.Google Scholar
Wielandt, Helmut. 1994. Mathematische Werke/Mathematical Works, vol. 1. Walter de Gruyter & Co., Berlin.Google Scholar
Wilson, Robert A. 2009. The Finite Simple Groups. Graduate Texts in Mathematics, vol. 251. Springer-Verlag London, Ltd., London.Google Scholar
Wilson, Robert, Walsh, Peter, Tripp, Jonathan, et al. (n.d.). ATLAS of Finite Group Representations - Version 3. http://brauer.maths.qmul.ac.uk/Atlas/v3/.Google Scholar
Wilson, Steve. 2003. A worthy family of semisymmetric graphs. Discrete Math., 271(1–3), 283294.Google Scholar
Wilson, Steve. 2008. Rose window graphs. Ars Math. Contemp., 1(1), 719.Google Scholar
Wilson, Steve, and Potočnik, Primož. 2016. Recipes for Edge-Transitive Tetravalent Graphs.Google Scholar
Witte, Dave. 1986. Cayley digraphs of prime-power order are Hamiltonian. J. Combin. Theory Ser. B, 40(1), 107112.Google Scholar
Witte, David. 1982. On Hamiltonian circuits in Cayley diagrams. Discrete Math., 38(1), 99108.Google Scholar
Witte, David, and Gallian, Joseph A. 1984. A survey: Hamiltonian cycles in Cayley graphs. Discrete Math., 51(3), 293304.Google Scholar
Witte Morris, Dave. 2015. Odd-order Cayley graphs with commutator subgroup of order pq are Hamiltonian. Ars Math. Contemp., 8(1), 128.Google Scholar
Witte Morris, Dave, and Wilk, Kirsten. 2020. Cayley graphs of order kp are Hamiltonian for k < 48. Art Discrete Appl. Math., 3(2), P2.02.Google Scholar
Wong, Warren J. 1967. Determination of a class of primitive permutation groups. Math. Z., 99, 235246.Google Scholar
Xu, Jing. 2008. Semiregular automorphisms of arc-transitive graphs with valency pq. European J. Combin., 29(3), 622629.Google Scholar
Xu, Ming Yao. 1992. Half-transitive graphs of prime-cube order. J. Algebraic Combin., 1(3), 275282.Google Scholar
Xu, Ming-Yao. 1998. Automorphism groups and isomorphisms of Cayley digraphs. Discrete Math., 182(1–3), 309319.Google Scholar
Xu, Yian. 2017. On constructing normal and non-normal Cayley graphs. Discrete Math., 340(12), 29722977.Google Scholar
Zhang, Jun-Yang. 2015. Vertex-transitive digraphs of order p5 are Hamiltonian. Electron. J. Combin., 22(1), P1.76.Google Scholar
Zhou, Jin-Xin. 2017. Edge-transitive almost self-complementary graphs. J. Combin. Theory Ser. B, 123, 215239.Google Scholar
Zhou, Jin-Xin, and Feng, Yan-Quan. 2010. Semisymmetric elementary abelian covers of the Heawood graph. Discrete Math., 310(24), 36583662.Google Scholar
Zhu, Yong Jin, Liu, Zhen Hong, and Yu, Zheng Guang. 1985. An improvement of Jackson’s result on Hamilton cycles in 2-connected regular graphs. Pages 237–247 of: Cycles in Graphs (Burnaby, B.C., 1982). North-Holland Math. Stud., vol. 115. North-Holland, Amsterdam.Google Scholar
Zhu, Yong Jin, Liu, Zhen Hong, and Yu, Zheng Guang. 1986a. 2-connected k-regular graphs [k ≥ 6] on at most 3k + 3 vertices are Hamiltonian. J. Systems Sci. Math. Sci., 6(1), 3649.Google Scholar
Zhu, Yong Jin, Liu, Zhen Hong, and Yu, Zheng Guang. 1986b. 2-connected k-regular graphs [k ≥ 6] on at most 3k + 3 vertices are Hamiltonian. II. J. Systems Sci. Math. Sci., 6(2), 136145.Google Scholar
Zsigmondy, K. 1892. Zur Theorie der Potenzreste. Monatsh. Math. Phys., 3(1), 265284.Google Scholar

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  • References
  • Ted Dobson, Univerza na Primorskem, Slovenia, Aleksander Malnič, Univerza na Primorskem, Slovenia, Dragan Marušič, Univerza na Primorskem, Slovenia
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