Quartic half-arc-transitive graphs with large vertex stabilizers

Abstract

A 1 2 - arc- transitive graph is a vertex- and edge- but not arc-transitive graph. In all previously known constructions of quartic 1 2 -arc-transitive graphs, vertex stabilizers are isomorphic to Z 2 , Z 2 2 or to D 8 . In this article, for each positive integer m ⩾ 1 , an infinite family of quartic 1 2 -arc-transitive graphs having vertex stabilizers isomorphic to Z 2 m is constructed.