SPECTRA OF CAYLEY GRAPHS

The adjacency spectrum of a graph Γ, which is denoted by Spec(Γ), is the multiset of eigenvalues of its adjacency matrix. We say that two graphs Γ and Γ 0 are cospectral if Spec(Γ) = Spec(Γ 0 ). In this talk we speak about some methods for constructing cospectral non-isomorphic Cayley graphs. In particular for each prime number p, p ≥ 23, we construct a large family of cospectral non-isomorphic Cayley graphs over the dihedral group of order 2p. This is a joint work with Shahrooz Janbaz and Meysam Ghahramani.