Spectra of Generalized Cayley Graphs on Finite Abelian Groups

Abstract

The spectra of generalized Cayley graphs of finite abelian groups are investigated in this paper. For a generalized Cayley graph [Formula: see text] of a finite group [Formula: see text], the canonical double covering of [Formula: see text] is the direct product [Formula: see text]. In this paper, integral generalized Cayley graphs on finite abelian groups are characterized, using the characterization of the spectra of integral Cayley graphs. As an application, the integral generalized Cayley graphs on [Formula: see text] and [Formula: see text] are investigated, where [Formula: see text] and [Formula: see text] are odd prime numbers.