On the order of semiregular automorphisms of cubic vertex-transitive graphs

Abstract

We prove that, if $\Gamma$ is a finite connected cubic vertex-transitive graph, then either there exists a semiregular automorphism of $\Gamma$ of order at least $6$, or the number of vertices of $\Gamma$ is bounded above by an absolute constant.

20 pages

References in corpus (3)

• Semiregular elements in cubic vertex-transitive graphs and the restricted Burnside problem
• On the number of fixed edges of automorphisms of vertex-transitive graphs of small valency
• On the Cayleyness of Praeger-Xu graphs