Cubic Non-Cayley Vertex-Transitive Bi-Cayley Graphs over a Regular $p$-Group

  • Jin-Xin Zhou
  • Yan-Quan Feng
Keywords: Bi-Cayley graph, Vertex-transitive, Automorphism group, Cayley graph


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 $p$.
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