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

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. ∗This work was supported in part by a grant from the Natural Science and Engineering Research Council of Canada. †Supported by UWA as part of the Australian Research Council grant DE130101001. the electronic journal of combinatorics 22(3) (2015), #P3.32 1