On the number of fixed points of automorphisms of vertex-transitive graphs of bounded valency
Potočnik, Primož, 1971- ; Spiga, Pablo
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.
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