Arc-Transitive Graphs of Valency 11 and Order Four Times an Odd Square-free Integer

In this paper, we classify connected arc-transitive graphs of valency 11 and of order [Formula: see text], where [Formula: see text] is an odd square-free integer. In particular, there are four infinite families of such graphs, which have a minimal arc-transitive automorphism group isomorphic to [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] separately, where [Formula: see text] is a prime. Moreover, examples for each class are constructed.