A classification of connected cubic vertex-transitive bi-Cayley graphs over semidihedral group

Abstract

A graph is said to be a bi-Cayley graph over a group H if there exists a subgroup of Aut(G) isomorphic to H acting semiregularly on its vertex set with two orbits. In this paper, we give a complete classification of connected cubic vertex-transitive bi-Cayley graphs over semidihedral group. As a byproduct, we construct a family of vertex-transitive non-Cayley graphs.