Classification of Cubic Symmetric Tricirculants

Abstract

A tricirculant is a graph admitting a non-identity automorphism having three cycles of equal length in its cycle decomposition. A graph is said to be symmetric if its automorphism group acts transitively on the set of its arcs. In this paper it is shown that the complete bipartite graph $K_{3,3}$, the Pappus graph, Tutte's 8-cage and the unique cubic symmetric graph of order 54 are the only connected cubic symmetric tricirculants.