On finite dual Cayley graphs

A Cayley graph Gamma on a group G is called a dual Cayley graph on G if the left regular representation of G is a subgroup of the automorphism group of Gamma (note that the right regular representation of G is always an automorphism group of Gamma). In this article, we study finite dual Cayley graphs regarding identification, construction, transitivity and such graphs with automorphism groups as small as possible. A few problems worth further research are also proposed.