Arc-transitive cubic graphs of order four times an odd square-free integer

Abstract

Xu, Zhang and Zhou [Chin. Ann. Math. 25B(4) (2004) 545–554] classified all arc-transitive cubic graphs of order [Formula: see text] with [Formula: see text] a prime. In this paper, we shall generalize this result by classifying all connected arc-transitive cubic graphs of order four times an odd square-free integer. It is shown that, for each of such graphs [Formula: see text], either the full automorphism group [Formula: see text] is isomorphic to [Formula: see text], [Formula: see text], [Formula: see text] or [Formula: see text], or [Formula: see text] is isomorphic to one of 5 graphs.