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

A graph Γ is said to be locally (G, 2)-arc transitive for G a subgroup of Aut(Γ) if, for any vertex α of Γ, G is transitive on the 2-arcs of Γ starting at α. In this talk, we will discuss general results involving locally (G, 2)-arc transitive graphs and recent progress toward the classification of the locally (G, 2)-arc transitive graphs, where Sz(q) ≤ G ≤ Aut(Sz(q)), q = 2 for some k ∈ N. In particular, we will discuss seven families of vertex-intransitive locally (G, 2)arc transitive graphs. Furthermore, for any graph Γ in one of these families, Sz(q) ≤ Aut(Γ) ≤ Aut(Sz(q)), and 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) 2arc 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 (“Finite two-arc transitive graphs admitting a Suzuki simple group,” Comm. Alg., 27(8):3727-3754, 1999), this completes the classification of locally 2-arc transitive graphs admitting a Suzuki simple group. This talk will be preceded by a Combinatorics Seminar entitled “Quasiprimitive group actions and graph quotients” that naturally complements (although is not required for!) this talk.