On 3-Transitive Graphs of Girth 6

A graph Γ is called (G, s)-transitive if G is a subgroup of Aut(Γ) acting transitively on the set of s-paths in Γ, but not on the set of (s + 1)-paths. The girth of Γ is the length of a shortest circuit in Γ (if Γ contains circuits). This paper gives a classification of (G, 3)-transitive graphs of girth 6 in which the stabilizer Gx in G of a vertex x contains a normal subgroup which induces a permutation group on the set of vertices adjacent to x isomorphic to PSL(n, q) with n ≥ 3.