A NOTE ON THE EIGENVALUES OF n-CAYLEY GRAPHS

A graph is called an n-Cayley graph over a group G if its automorphism contains a semi-regular subgroup isomorphic to G with n orbits. Every n-Cayley graph over a group G is completely determined by n(2) suitable subsets of G. If each of these subsets is a union of conjugacy classes of G, then it is called a quasi-abelian n-Cayley graph over G. In this paper, we determine the characteristic polynomial of quasi-abelian n-Cayley graphs. Then we exactly determine the eigenvalues and the number of closed walks of quasi-abelian semi-Cayley graphs. Furthermore, we construct some integral graphs.