A classification of tetravalent connected vertex-transitive bi-dicirculants

Abstract

A graph is said to be a bi-Cayley graph over a group H if it admits H as a group of automorphisms acting semiregularly on its vertex-set with two orbits of equal size. A bi-Cayley graph over a dicyclic group is called a bi-dicirculant. We give a classification of tetravalent connected vertex-transitive bi-dicirculants in this paper. As a byproduct, we prove that all connected tetravalent vertex-transitive bi-dicirculants are Cayley graphs.