On the Laplacian and signless Laplacian polynomials of graphs with semiregular automorphisms

A graph Gamma is called n-Cayley graph over a group G if Aut(Gamma) has a semiregular subgroup isomorphic to G with n orbits (of equal size). In this paper, we give a decomposition of the Laplacian and signless Laplacian polynomials of n-Cayley graphs in terms of irreducible representations of G. Also, we construct several families of graphs with integral Laplacian and signless Laplacian spectrum.