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 is an element of 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.