Classification of cubic vertex-transitive tricirculants

Authors

  • Primož Potočnik University of Ljubljana, Slovenia
  • Micael Toledo Institute of Mathematics, Physics and Mechanics, Ljubljana

DOI:

https://doi.org/10.26493/1855-3974.1815.b52

Keywords:

Graph, cubic, semiregular automorphism, tricirculant, vertex-transitive

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 Möbius 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.

Published

2020-05-29

Issue

Section

Articles