Semiregular automorphisms of cubic vertex-transitive graphs
Combinatorics
2014-01-14 v1
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.
Cite
@article{arxiv.1401.2940,
title = {Semiregular automorphisms of cubic vertex-transitive graphs},
author = {Joy Morris and Pablo Spiga and Gabriel Verret},
journal= {arXiv preprint arXiv:1401.2940},
year = {2014}
}
Comments
This paper settles Problem 6.3 in P. Cameron, M. Giudici, G. Jones, W. Kantor, M. Klin, D. Maru\v{s}i\v{c}, L. A. Nowitz, Transitive permutation groups without semiregular subgroups, J. London Math. Soc. 66 (2002), 325--333