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

##### 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