Finite cubic graphs admitting an cyclic group of automorphisms with at most three orbits on vertices
Combinatorics
2020-03-12 v1
Abstract
The theory of voltage graphs has become a standard tool in the study graphs admitting a semiregular group of automorphisms. We introduce the notion of a cyclic generalised voltage graph to extend the scope of this theory to graphs admitting a cyclic group of automorphism that may not be semiregular. We use this new tool to classify all cubic graphs admitting a cyclic group of automorphisms with at most three vertex-orbits and we characterise vertextransitivity for each of these classes. In particular, we show that a cubic vertex-transitive graph admitting a cyclic group of automorphisms with at most three orbits on vertices either belongs to one of 5 infinite families or is isomorphic to the well-know Tutte-Coxeter graph.
Keywords
Cite
@article{arxiv.2003.05186,
title = {Finite cubic graphs admitting an cyclic group of automorphisms with at most three orbits on vertices},
author = {Primoz Potocnik and Micael Toledo},
journal= {arXiv preprint arXiv:2003.05186},
year = {2020}
}