On 3-transitive graphs of girth 6 (Q1338320)

A finite, connected, undirected graph \(\Gamma\) is said to be \((G,s)\)- transitive if \(G\leq \Aut\Gamma\) acts transitively on \(s\)-paths but not on \((s+ 1)\)-paths. Taking advantage of a previous result by \textit{A. A. Ivanov} [Math. USSR, Izv. 35, No. 2, 307-335 (1990; Zbl 0706.05026)], this paper completes the classification of \((G,3)\)-transitive graphs \(\Gamma\) of girth 6, satisfying \(\text{PSL}(n, q)\leq G_ v^{\Gamma(v)}\leq \text{P}\Gamma\text{L}(n, q),\) where \(n\geq 3\). All such \(\Gamma\) are incidence graphs of subspaces of dimensions \(n-2\) and \(n-1\) of \(\text{PG}(2n- 2, q)\).