Hermitian Adjacency Spectrum of Cayley Digraphs over Dihedral Group

We first study the spectrum of Hermitian adjacency matrix (H-spectrum) of Cayley digraphs X(D-2n, S) on dihedral group D-2n, with vertical bar S vertical bar = 3. Then we show that all Cayley digraphs X(D-2p,S) with vertical bar S vertical bar = 3 and p odd prime are Cay-DS, namely, for any Cayley digraph X(D-2p, T), X (D-2p, T) and X(D-2p, S) having the same H-spectrum implies that they are isomorphic.