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Buildings and s-Transitive Graphs

  • Richard M. WeissEmail author
Chapter
  • 750 Downloads
Part of the Fields Institute Communications book series (FIC, volume 70)

Abstract

A graph is s-transitive if its automorphism group acts transitively on the set of paths of length s. This is a notion due to William Tutte who showed in 1947 that a finite trivalent graph can never be 6-transitive. We examine connections between the theory of s-transitive graphs and the classification of Moufang polygons, a class of graphs exhibiting “local” s-transitivity for large values of s. Moufang polygons are examples of buildings. Both of these notions were introduced by Jacques Tits in the study of algebraic groups. We give an overview of Tits’ classification results in the theory of spherical buildings (which include the classification of Moufang polygons as a special case) and describe, in particular, the classification of finite buildings.

Keywords

Building s-transitive graph Moufang polygon 

Subject Classifications

20E42 51E24 

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of MathematicsTufts UniversityMedfordUSA

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