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3 - The Cost of Distinguishing Graphs

Published online by Cambridge University Press:  20 July 2017

Debra Boutin
Affiliation:
Hamilton College, Clinton, NY 13323, USA
Wilfried Imrich
Affiliation:
Montanuniversität Leoben, 8700 Leoben, Austria
Tullio Ceccherini-Silberstein
Affiliation:
Università degli Studi del Sannio, Italy
Maura Salvatori
Affiliation:
Università degli Studi di Milano
Ecaterina Sava-Huss
Affiliation:
Cornell University, New York
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Publisher: Cambridge University Press
Print publication year: 2017

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References

[1] M. O., Albertson, Distinguishing Cartesian powers of graphs, Electron. J. Combin. 12 (2005), Note 17, 5 pp.Google Scholar
[2] M. O., Albertson and D. L., Boutin, Using determining sets to distinguish Kneser graphs, Electron. J. Combin. 14 (2007), no. 1, Research Paper 20, 9 pp.Google Scholar
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[7] D. L., Boutin, The cost of 2-distinguishing selected Kneser graphs and hypercubes, J. Combin. Math. Combin. Comput. 85 (2013), 161–71.Google Scholar
[8] D. L., Boutin, The cost of 2-distinguishing Cartesian powers, Electron. J. Combin. 20 (2013), no. 1, Paper 74, 13 pp.Google Scholar
[9] B., Bogstad and L. J., Cowen, The distinguishing number of the hypercube, Discrete Math. 283 (2004), 29–35.Google Scholar
[10] D. L., Boutin and W., Imrich, Infinite graphs with finite 2-distinguishing cost, Electron. J. Combin., forthcoming.
[11] R., Diestel, Graph Theory. Electronic edition. Springer, 2005.
[12] M., Goff, Personal communication.
[13] R., Hammack, W., Imrich, and S., Klavžar, Handbook of product graphs, second edition. Discrete Mathematics and its Applications (Boca Raton). CRC Press, Boca Raton, FL, 2011. xviii+518 pp.
[14] R., Halin, Automorphisms and endomorphisms of infinite locally finite graphs, Abh. Math. Sem. Univ. Hamburg, 39 (1973), 251–83.Google Scholar
[15] W., Imrich, S., Klavar, and V., Trofimov, Distinguishing infinite graphs, Electron. J. Combin. 14 (2007), no. 1, Research Paper 36, 12 pp.Google Scholar
[16] W., Imrich, S. M., Smith, T.W., Tucker, and M. E., Watkins, Infinite motion and the distinguishing number of graphs and groups, J. Algebraic Comb., DOI 10.1007/s10801-014-0529-2.
[17] T., Fukuda, S., Negami, and T. W., Tucker, 3-connected planar graphs are 2-distinguishable with few exceptions, Yokohama Math. J. 54 (2008), no. 2, 143–53.Google Scholar
[18] W., Imrich and S., Klavžar, Distinguishing Cartesian powers of graphs, J. Graph Theory 53 (2006), no. 3, 250–60.Google Scholar
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[20] F., Lehner, Distinguishing graphs with intermediate growth, Combinatorica, 2015, 36 (2016), no. 3, 333–47.Google Scholar
[21] S. M., Smith, T. W., Tucker, and M. E., Watkins, Distinguishability of infinite groups and graphs, Electron. J. Combin. 19 (2012), no. 2, Paper 27, 10 pp.Google Scholar
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