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. (2022). On the number of fixed edges of automorphisms of vertex-transitive graphs of small valency. JOURNAL OF ALGEBRAIC COMBINATORICS [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
2022

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.
Articolo in rivista - Articolo scientifico
Arc-transitive; fixed-points; Valency 3; Valency 4; Vertex-transitive;
English
Barbieri, M., Grazian, V., Spiga, P. (2022). On the number of fixed edges of automorphisms of vertex-transitive graphs of small valency. JOURNAL OF ALGEBRAIC COMBINATORICS [10.1007/s10801-022-01176-5].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/393091
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