Classification of cubic vertex-transitive tricirculants

Primož Potočnik, Micael Toledo

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

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

ISSN: 1855-3974

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