On integral Cayley sum graphs

Let S be a subset of a finite abelian group G . The Cayley sum graph Cay + ( G, S ) of G with respect to S is a graph whose vertex set is G and two vertices g and h are joined by an edge if and only if g + h ∈ S . We call a finite abelian group G a Cayley sum integral group if for every subset S of G , Cay + ( G, S ) is integral i.e., all eigenvalues of its adjacency matrix are integers. In this paper, we prove that all Cayley sum integral groups are represented by Z 3 and Zn 2 n , n ≥ 1, where Z k is the group of integers modulo k . Also, we classify simple connected cubic integral Cayley sum graphs.