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ON THE ORDER OF ARC-STABILISERS IN ARC-TRANSITIVE GRAPHS, II
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 87 / Issue 3 / June 2013
- Published online by Cambridge University Press:
- 02 August 2012, pp. 441-447
- Print publication:
- June 2013
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- Article
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Let
$\Gamma $ be a 
$G$-vertex-transitive graph and let 
$(u,v)$ be an arc of 
$\Gamma $. It is known that if the local action 
$G_v^{\Gamma (v)}$ (the permutation group induced by 
$G_v$ on 
$\Gamma (v)$) is permutation isomorphic to the dihedral group of degree four, then either 
$|G_{uv}|$ is ‘small’ with respect to the order of 
$\Gamma $ or 
$\Gamma $is one of a family of well-understood graphs. In this paper, we generalise this result to a wider class of local actions.
