On finite groups all of whose cubic Cayley graphs are integral

Abstract

For any positive integer [Formula: see text], let [Formula: see text] denote the set of finite groups [Formula: see text] such that all Cayley graphs [Formula: see text] are integral whenever [Formula: see text]. Estélyi and Kovács [On groups all of whose undirected Cayley graphs of bounded valency are integral, Electron. J. Combin. 21 (2014) #P4.45.] classified [Formula: see text] for each [Formula: see text]. In this paper, we characterize the finite groups each of whose cubic Cayley graphs is integral. Moreover, the class [Formula: see text] is characterized. As an application, the classification of [Formula: see text] is obtained again, where [Formula: see text].