We prove that, if Γ is a finite connected cubic vertex-transitive graph, then either there exists a semiregular automorphism of Γ of order at least 6, or the number of vertices of Γ is bounded above by an absolute constant.
Barbieri, M., Grazian, V., Spiga, P. (2025). On the order of semiregular automorphisms of cubic vertex-transitive graphs. EUROPEAN JOURNAL OF COMBINATORICS, 124(February 2025) [10.1016/j.ejc.2024.104091].
On the order of semiregular automorphisms of cubic vertex-transitive graphs
Spiga P.
2025
Abstract
We prove that, if Γ is a finite connected cubic vertex-transitive graph, then either there exists a semiregular automorphism of Γ of order at least 6, or the number of vertices of Γ is bounded above by an absolute constant.
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