Integral Cayley sum graphs and groups

Abstract

For any positive integer k, let Ak denote the set of finite abelian groups G such that for any subgroup H of G all Cayley sum graphs CayS(H,S) are integral if |S| = k. A finite abelian group G is called Cayley sum integral if for any subgroup H of G all Cayley sum graphs on H are integral. In this paper, the classes A2 and A3 are classified. As an application, we determine all finite Cayley sum integral groups.