Bounding the order of the vertex-stabiliser in 3-valent vertex-transitive and 4-valent arc-transitive graphs

P. Potočnik; P. Spiga; Gabriel Verret

doi:10.1016/j.jctb.2014.10.002

Bounding the order of the vertex-stabiliser in 3-valent vertex-transitive and 4-valent arc-transitive graphs

P. Potočnik, P. Spiga, Gabriel Verret

Research output: Contribution to journal › Article › peer-review

23 Citations (Scopus)

Abstract

© 2014 Elsevier Inc. The main result of this paper is that, if Γ is a connected 4-valent G-arc-transitive graph and v is a vertex of Γ, then either Γ is part of a well-understood infinite family of graphs, or |Gv|≤2436 or 2|Gv|log2(|Gv|/2)≤|VΓ| and that this last bound is tight. As a corollary, we get a similar result for 3-valent vertex-transitive graphs.

Original language	English
Pages (from-to)	148-180
Number of pages	33
Journal	Journal of Combinatorial Theory. Series B
Volume	111
DOIs	https://doi.org/10.1016/j.jctb.2014.10.002
Publication status	Published - Mar 2015

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10.1016/j.jctb.2014.10.002

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abstract = "{\textcopyright} 2014 Elsevier Inc. The main result of this paper is that, if Γ is a connected 4-valent G-arc-transitive graph and v is a vertex of Γ, then either Γ is part of a well-understood infinite family of graphs, or |Gv|≤2436 or 2|Gv|log2(|Gv|/2)≤|VΓ| and that this last bound is tight. As a corollary, we get a similar result for 3-valent vertex-transitive graphs.",

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AU - Verret, Gabriel

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AB - © 2014 Elsevier Inc. The main result of this paper is that, if Γ is a connected 4-valent G-arc-transitive graph and v is a vertex of Γ, then either Γ is part of a well-understood infinite family of graphs, or |Gv|≤2436 or 2|Gv|log2(|Gv|/2)≤|VΓ| and that this last bound is tight. As a corollary, we get a similar result for 3-valent vertex-transitive graphs.

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JF - Journal of combinatorial Theory Series B

ER -

Bounding the order of the vertex-stabiliser in 3-valent vertex-transitive and 4-valent arc-transitive graphs

Abstract

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