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Tang, Lang; Cheng, Tao; Liu, Weijun; Feng, Lihua
Discrete mathematics, December 2021, 2021-12-00, Volume: 344, Issue: 12Journal Article
For a finite group G and an inverse closed subset S⊆G∖{e}, the Cayley graph X(G,S) has vertex set G and two vertices x,y∈G are adjacent if and only if xy−1∈S. Two graphs are called cospectral if their adjacency matrices have the same spectrum. Let p≥3 be a prime number and T4p be the dicyclic group of order 4p. In this paper, with the help of the characters from representation theory, we construct a large family of pairwise non-isomorphic and cospectral Cayley graphs over the dicyclic group T4p with p≥23, and find several pairs of non-isomorphic and cospectral Cayley graphs for 5≤p≤19.
