Generalized polygons and \(s\)-transitive graphs. (English) Zbl 0751.05051

Weiss, Richard

Finite geometries, buildings, and related topics, Pap. Conf., Pingree Park/CO (USA) 1988, 95-103 (1990).

[For the entire collection see Zbl 0741.00065.]
In [Proc. Camb. Phil. Soc. 43, 459-474 (1948; Zbl 0029.42401) and Can. J. Math. 11, 621-624 (1959; Zbl 0093.377)] W. T. Tutte proved that if a finite 3-valent graph is \(s\)-transitive, then \(s\leq 5\). The author gives, in his words, “a brief survey of various efforts to extend and apply this and some related \(\ldots\) results of [J.] Tits.” Many of the author’s papers and joint papers since 1978 and Tits’ results are cited. Most relate to the weaker condition of local \(s\)-transitivity and to generalized polygons as examples of locally \(s\)-transitive graphs.

Reviewer: M.E.Watkins (Syracuse)

MSC:

05C25	Graphs and abstract algebra (groups, rings, fields, etc.)
51E12	Generalized quadrangles and generalized polygons in finite geometry
20B25	Finite automorphism groups of algebraic, geometric, or combinatorial structures

Keywords:

generalized polygons; \(s\)-transitive graphs; Moufang; BN-pair; amalgam; local \(s\)-transitivity