Generalized Polygons and s-Transitive Graphs
Richard M. Weiss · 1990
Abstract Stabilizer Gacts transitively on the set of s-paths beginning at x.If, in addition, Gacts transitively on the vertex set off, and hence on the set of alls-paths in r, then f is called s-transitivewith respect to G.We will give here a brief survey of various efforts to extend and apply this and some related (but historically independent) results of Tits. As these developments include the entire theory of amalgams opened up byD. Goldschmidt’s seminal paper [8] on locally s-transitive trivalent graphs, our choice of results will, of necessity, be very selective. In general, we will describe results which are of a more graph theoretical nature. The reader is referred to (22] for an earlier report on s-transitive graphs.