Semiregular automorphisms of cubic vertex-transitive graphs

Abstract

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 paper settles Problem 6.3 in P. Cameron, M. Giudici, G. Jones, W. Kantor, M. Klin, D. Marušič, L. A. Nowitz, Transitive permutation groups without semiregular subgroups, J. London Math. Soc. 66 (2002), 325--333