English

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.

Keywords

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}
}
R2 v1 2026-06-23T06:38:21.041Z