For any positive integer k, let Gkβ denote the set of finite
groups G such that all Cayley graphs Cay(G,S) are integral whenever
β£Sβ£β€k. EsteΛlyi and KovaΛcs \cite{EK14}
classified Gkβ for each kβ₯4. In this paper, we characterize
the finite groups each of whose cubic Cayley graphs is integral. Moreover, the
class G3β is characterized. As an application, the classification
of Gkβ is obtained again, where kβ₯4.Comment: 11 pages, accepted by Journal of Algebra and its Applications on June
201