GCI-groups in the alternating groups

The concept of generalized Cayley graphs was first introduced by Marui etal. (1992). In this paper, we will study the isomorphism problem of generalized Cayley graphs. Similar to the concept of CI-groups corresponding to Cayley graphs, we define the so-called GCI-groups corresponding to generalized Cayley graphs. The main result we show is that the alternating group An is a GCI-group if and only if n=4.