On the number of fixed points of automorphisms of vertex-transitive graphs of bounded valency

Abstract

The main result of this paper is that, if $\Gamma$ is a finite connected $4$-valent arc-transitive graph, then either $\Gamma$ is part of a well-understood family of graphs, or every non-identity automorphism of $\Gamma$ fixes at most $1/3$ of the vertices. As a corollary, we get a similar result for $3$-valent vertex-transitive graphs. Based on these results we propose a conjecture on the number of fixed points of non-identity automorphisms of vertex-transitive graphs of bounded valency.

23 pages The orginal version has been split into two parts. This part has more details on the graph theoretic application

References in corpus (2)

• Graph Isomorphism in Quasipolynomial Time
• Recipes for Edge-Transitive Tetravalent Graphs

Cited by in corpus (1)

• On minimal degree of transitive permutation groups with stabiliser being a $2$-group