-
Jin-Xin Zhou
-
Yan-Quan Feng
Keywords:
Bi-Cayley graph, Vertex-transitive, Automorphism group, Cayley graph
Abstract
A bi-Cayley graph is a graph which admits a semiregular group of automorphisms with two orbits of equal size. In this paper, we give a characterization of cubic non-Cayley vertex-transitive bi-Cayley graphs over a regular $p$-group, where $p>5$ is an odd prime. As an application, a classification of cubic non-Cayley vertex-transitive graphs of order $2p^3$ is given for each prime $p$.