On the order of arc-stabilisers in arc-transitive graphs with prescribed local group

Abstract

Let $Γ$ be a connected $G$-arc-transitive graph, let $uv$ be an arc of $Γ$ and let $L$ be the permutation group induced by the action of the vertex-stabiliser $G_v$ on the neighbourhood $Γ(v)$. We study the problem of bounding $|G_{uv}|$ in terms of $L$ and the order of $Γ$.

17 pages, 1 table