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Constructing families of cospectral regular graphs

  • M. Haythorpe (a1) and A. Newcombe (a1)


A set of graphs are called cospectral if their adjacency matrices have the same characteristic polynomial. In this paper we introduce a simple method for constructing infinite families of cospectral regular graphs. The construction is valid for special cases of a property introduced by Schwenk. For the case of cubic (3-regular) graphs, computational results are given which show that the construction generates a large proportion of the cubic graphs, which are cospectral with another cubic graph.


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Research partially supported by ARC Discovery Grant DP150100618.



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[1]Abiad, A. and Haemers, W. H. (2012) Cospectral graphs and regular orthogonal matrices of level 2. Electron. J. Combin. 19 1329.
[2]Baniasadi, P., Ejov, V., Filar, J. A. and Haythorpe, M. (2016) Genetic Theory for Cubic Graphs, Springer Briefs inOperations Research, Springer.
[3]Bapat, R. B. and Karimi, M. (2016) Construction of cospectral regular graphs. Mat. Vesnik 68 6676.
[4]Blazsik, Z. L., Cummings, J. and Haemers, W. H. (2015) Cospectral regular graphs with and without a perfect matching. Discrete Math. 338 199201.
[5]Borkar, V. S., Ejov, V., Filar, J. A. and Nguyen, G. T. (2012) Hamiltonian Cycle Problem and Markov Chains, Springer Science & Business Media.
[6]Cvetkovic, D., Rowlinson, P. and Simic, S. (1997) Eigenspaces of Graphs, Cambridge University Press.
[7]Filar, J. A., Gupta, A. and Lucas, S. K. (2005) Connected cospectral graphs are not necessarily both Hamiltonian. Aust. Math. Soc. Gaz. 32 193.
[8]Godsil, C. D. (1992) Walk generating functions, Christophell–Darboux identities and the adjacency matrix of a graph. Combin. Probab. Comput. 1 1325.
[9]Godsil, C. D. and McKay, B. D. (1982) Construction of cospectral graphs. Aequationes Math. 25 257268.
[10]Rowlinson, P. (1993) The characteristic polynomials of modified graphs. Discrete Appl. Math. 67 209219.
[11]Schwenk, A. J. (1979) Removal-cospectral sets of vertices in a graph. In 10th Southeastern International Conference on Combinatorics, Graph Theory and Computing, pp. 849860.

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Constructing families of cospectral regular graphs

  • M. Haythorpe (a1) and A. Newcombe (a1)


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