On the number of fixed edges of automorphisms of vertex-transitive graphs of small valency
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| Acceso en línea: | |
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| _version_ | 1866929638351044608 |
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| author | Barbieri, Marco Grazian, Valentina Spiga, Pablo |
| author_facet | Barbieri, Marco Grazian, Valentina Spiga, Pablo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_11434 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On the number of fixed edges of automorphisms of vertex-transitive graphs of small valency Barbieri, Marco Grazian, Valentina Spiga, Pablo Combinatorics Group Theory 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. |
| title | On the number of fixed edges of automorphisms of vertex-transitive graphs of small valency |
| topic | Combinatorics Group Theory |
| url | https://arxiv.org/abs/2202.11434 |