Cubic Vertex-Transitive Graphs Admitting Automorphisms of Large Order

Abstract

A connected graph of order n admitting a semiregular automorphism of order n/k is called a k-multicirculant. Highly symmetric multicirculants of small valency have been extensively studied, and several classification results exist for cubic vertex- and arc-transitive multicirculants. In this paper, we study the broader class of cubic vertex-transitive graphs of order n admitting an automorphism of order n/3 or larger that may not be semiregular. In particular, we show that any such graph is either a k-multicirculant for some $$k \le 3$$ k ≤ 3 , or it belongs to an infinite family of graphs of girth 6.