The locally 2-arc transitive graphs admitting an almost simple group of Suzuki type

Abstract

In this paper, seven families of vertex-intransitive locally (G,2)-arc transitive graphs are constructed, where Sz(q)⩽G⩽Aut(Sz(q)), q=22k+1 for some k∈N. It is then shown that for any graph Γ in one of these families, Sz(q)⩽Aut(Γ)⩽Aut(Sz(q)) and that the only locally 2-arc transitive graphs admitting an almost simple group of Suzuki type whose vertices all have valency at least three are (i) graphs in these seven families, (ii) (vertex transitive) 2-arc transitive graphs admitting an almost simple group of Suzuki type, or (iii) double covers of the graphs in (ii). Since the graphs in (ii) have been classified by Fang and Praeger (1999) [6], this completes the classification of locally 2-arc transitive graphs admitting a Suzuki simple group