Vertex-transitive generalized Cayley graphs which are not Cayley graphs

The concept of generalized Cayley graphs was introduced by Marušič et al. (1992), where it was asked if there exists a vertex-transitive generalized Cayley graph which is not a Cayley graph. In this paper the question is answered in the affirmative with a construction of two infinite families of such graphs. It is also proven that every generalized Cayley graph admits a semiregular automorphism.