Which cayley graphs are integral

Abstract

Let G be a non-trivial group, S⊆G \ {1} and S = S-1 := {s-1 | s⊆ S}. The Cayley graph of G denoted by Γ(S : G) is a graph with vertex set G and two vertices a and b are adjacent if ab -1 ⊆ S. A graph is called integral, if its adjacency eigenvalues are integers. In this paper we determine all connected cubic integral Cayley graphs. We also introduce some infinite families of connected integral Cayley graphs.