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1 results

  • Constructing families of cospectral regular graphs

  • Part of
  • M. Haythorpe, A. Newcombe
  • Journal:
    Combinatorics, Probability and Computing / Volume 29 / Issue 5 / September 2020
    Published online by Cambridge University Press:
    30 June 2020, pp. 664-671

  • 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.