Construction of Cospectral Cayley Digraphs over Dihedral Group D 6p

Let [Formula: see text] be a finite group and [Formula: see text], where [Formula: see text] denotes the identity element of [Formula: see text]. The Cayley digraph [Formula: see text] of [Formula: see text] over the set [Formula: see text] is the graph with vertex set [Formula: see text] and edge set [Formula: see text]. Two graphs are called cospectral if their adjacency matrices have the same spectrum. We construct a large family of cospectral non-isomorphic Cayley digraphs over the dihedral group of order [Formula: see text] for [Formula: see text].