Semiregular Automorphisms of Cubic Vertex-Transitive Graphs and the Abelian Normal Quotient Method

Joy Morris, Pablo Spiga, Gabriel Verret


We characterise connected cubic graphs admitting a vertex-transitive group of automorphisms with an abelian normal subgroup that is not semiregular. We illustrate the utility of this result by using it to prove that the order of a semiregular subgroup of maximum order in a vertex-transitive group of automorphisms of a connected cubic graph grows with the order of the graph.


Cubic graphs; vertex-transitive graphs; semiregular automorphisms

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