Constructing families of cospectral regular graphs

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Abstract

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.
Original languageEnglish
Pages (from-to)664-671
Number of pages8
JournalCombinatorics, Probability and Computing
Volume29
Issue number5
DOIs
Publication statusPublished - Sep 2020

Keywords

  • cospectral regular graphs
  • spectral graph theory
  • Constructing graphs

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