On fixity of arc-transitive graphs

Florian Lehner, Primož Potočnik, Pablo Spiga*

*Corresponding author for this work

Research output: Contribution to journalArticle

Abstract

The relative fixity of a permutation group is the maximum proportion of the points fixed by a non-trivial element of the group, and the relative fixity of a graph is the relative fixity of its automorphism group, viewed as a permutation group on the vertex-set of the graph. We prove in this paper that the relative fixity of connected 2-arc-transitive graphs of a fixed valence tends to 0 as the number of vertices grows to infinity. We prove the same result for the class of arc-transitive graphs of a fixed prime valence, and more generally, for any class of arc-transitive locally-L graphs, where L is a fixed quasiprimitive graph-restrictive permutation group.

Original languageEnglish
JournalScience China / Mathematics
DOIs
Publication statusAccepted/In press - 2021

Keywords

  • 20B25
  • arc-transitive
  • automorphism group
  • fixed points
  • fixity
  • graph
  • minimal degree
  • permutation group
  • vertex-transitive

ASJC Scopus subject areas

  • Mathematics(all)

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