Isomorphisms of generalized Cayley graphs

In this paper, we investigate the isomorphism problems of the generalized Cayley graphs, which are generalizations of the traditional Cayley graphs. We find that there are two types of natural isomorphisms for the generalized Cayley graphs. We also study the GCI-groups among the generalized Cayley graphs, and the Cayley regressions of some groups. We mainly showed that, for an odd prime power n, Z(2)(n) (resp. D-2n) is a restricted GCI-group if D-2(n) (resp. Z(2n)) is a CI-group. We also obtain that the cyclic group of order 2(n) is a 4-quasi-Cayley regression if and only if n = 3.