A large family of cospectral Cayley graphs over dihedral groups.

The adjacency spectrum of a graph Γ , which is denoted by S p e c ( Γ ) , is the multiset of eigenvalues of its adjacency matrix. We say that two graphs Γ and Γ ′ are cospectral if S p e c ( Γ ) = S p e c ( 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 2 p . [ABSTRACT FROM AUTHOR]