Quasi-abelian Cayley graphs and parsons graphs

Abstract

Let G be a finite group, and S a subset of G with 1 ∉ S and S-1 = S. If S is a union of conjugacy classes of G, then the Cayley graph X = Cay(G, S) on G with respect to S is called quasi-abelian. In this paper we prove that any connected quasi-abelian Cayley graph is hamiltonian (Theorem 2). As a consequence, we prove that Zaks' three conjectures on Parsons graphs are true, with one exception. © 1997 Academic Press Limited.