Cubic Vertex-Transitive Non-Cayley Graphs of Order $8p$

  • Jin-Xin Zhou
  • Yan-Quan Feng
Keywords: Cayley graphs, Vertex-transitive graphs, Automorphism groups


A graph is vertex-transitive if its automorphism group acts transitively on its vertices. A vertex-transitive graph is a Cayley graph if its automorphism group contains a subgroup acting regularly on its vertices. In this paper, the cubic vertex-transitive non-Cayley graphs of order $8p$ are classified for each prime $p$. It follows from this classification that there are two sporadic and two infinite families of such graphs, of which the sporadic ones have order $56$,  one infinite family exists for every prime $p>3$ and the other family exists if and only if $p\equiv 1\mod 4$. For each family there is a unique graph for a given order.
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