Classification of cubic vertex-transitive tricirculants
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.
Keywords
Graph, cubic, semiregular automorphism, tricirculant, vertex-transitive
DOI: https://doi.org/10.26493/1855-3974.1815.b52
ISSN: 1855-3974
Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications