A large family of cospectral Cayley graphs over dihedral groups

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′ are cospectral if Spec(Γ)=Spec(Γ′). In this paper 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.