Semiregular automorphisms of cubic vertex-transitive graphs and the abelian normal quotient method
Electronic Journal of Combinatorics
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.
Sherpa Romeo green journal. Open access
Cubic graphs , Vertex-transitive graphs , Semiregular automorphisms
Morris, J., Spiga, P., & Verret, G. (2015). Semiregular automorphisms of cubic vertex-transitive graphs and the abelian normal quotient method. Electronic Journal of Combinatorics, 22(3), P3.32