We prove that, if Γ is a finite connected 3-valent vertex-transitive, or 4-valent vertex- and edge-transitive graph, then either Γ is part of a well-understood family of graphs, or every non-identity automorphism of Γ fixes at most 1/3 of the edges. This answers a question proposed by Primož Potočnik and the third author.
Barbieri, M., Grazian, V., Spiga, P. (2023). On the number of fixed edges of automorphisms of vertex-transitive graphs of small valency. JOURNAL OF ALGEBRAIC COMBINATORICS, 57(1), 329-348 [10.1007/s10801-022-01176-5].
On the number of fixed edges of automorphisms of vertex-transitive graphs of small valency
Grazian, Valentina;Spiga, Pablo
2023
Abstract
We prove that, if Γ is a finite connected 3-valent vertex-transitive, or 4-valent vertex- and edge-transitive graph, then either Γ is part of a well-understood family of graphs, or every non-identity automorphism of Γ fixes at most 1/3 of the edges. This answers a question proposed by Primož Potočnik and the third author.
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