Distance-transitive graphs and generalized polygons
Let G be a group acting distance-transitively and faithfully on a finite graph \(\Gamma\) of valency \(q+1\). Suppose as well that G acts transitively on the set of paths of length s in \(\Gamma\) for some \(s\geq 4\). Then \(\Gamma\) is the incidence graph of a generalized (s-1)-gon and G is isomorphic to a suitable subgroup of \(aut(L_ 3(q))\) with \(s=4\), \(aut(Sp_ 4(q))\) with \(s=5\) and q a power of two or \(aut(G_ 2(q))\) with \(s=7\) and q a power of three, or \(\Gamma\) is isomorphic to one of two exceptional graphs.
scientific article; zbMATH DE number 3906525