Generalized Cayley graphs were introduced by Marusic etal in 1992. Ademir Hujdurovic etal proved that there are infinitely many vertex-transitive generalized Cayley graphs which are not Cayley graphs. In fact, line graph of Petersen graph is one such example. They also prove that generalized Cayley graphs admits semi-regular automorphism.
It is obvious generalized Cayley graph $GC(G,S,\alpha)$ is $|S|$-regular. Moreover, there are examples of non-vertex-transitive generalized Cayley graphs.
My question is: Does there exist any vertex-transitive graph which is not generalized Cayley?
One answer to this is Petersen graph. For if it is generalized Cayley graph of order $10$ ($=2p$), it must be Cayley.
I am looking for some more such examples?