2021/10/11 by Haythorpe, Michael, Newcombe, Alex
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2110.04985
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.