Classification of cubic vertex-transitive tricirculants
Combinatorics
2018-12-12 v1
Abstract
A finite graph is called a tricirculant if admits a cyclic group of automorphism which has precisely three orbits on the vertex-set of the graph, all of equal size. We classify all finite connected cubic vertex-transitive tricirculants. We show that except for some small exceptions of order less than 54, each of these graphs is either a prism of order 6k with k odd, a M\"obius ladder, or it falls into one of two infinite families, each family containing one graph for every order of the form 6k with k odd.
Cite
@article{arxiv.1812.04153,
title = {Classification of cubic vertex-transitive tricirculants},
author = {Primož Potočnik and Micael Toledo},
journal= {arXiv preprint arXiv:1812.04153},
year = {2018}
}