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

Abstract

The main result of this paper is that, if $\Gamma$ is a connected 4-valent $G$-arc-transitive graph and $v$ is a vertex of $\Gamma$, then either $\Gamma$ is one of a well understood infinite family of graphs, or $|G_v|\le 2^4{3}^6$ 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.

arXiv comment37 pages

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