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 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.