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arXiv · 1010.2546

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

Primoz Potocnik·Pablo Spiga·Gabriel Verret
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Abstract

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 one of a well understood infinite family of graphs, or $|G_v|\leq 2^43^6$ or $2|G_v|\log_2(|G_v|/2)\leq |\VΓ|$ 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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Primoz Potocnik, Pablo Spiga, Gabriel Verret. 2010-10-13. Bounding the order of the vertex-stabiliser in 3-valent vertex-transitive and 4-valent arc-transitive graphs. https://arxiv.org/abs/1010.2546

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