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ON THE ORDER OF ARC-STABILISERS IN ARC-TRANSITIVE GRAPHS, II

Part of: Permutation groups

Published online by Cambridge University Press:  02 August 2012

GABRIEL VERRET
GABRIEL VERRET*
Affiliation:
FAMNIT, University of Primorska, Glagoljaška 8, 6000 Koper, Slovenia (email: [email protected])
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Abstract

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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.

Keywords

arc-transitive graphsgraph-restrictive grouplocal action

MSC classification

Secondary: 20B25: Finite automorphism groups of algebraic, geometric, or combinatorial structures
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 87 , Issue 3 , June 2013 , pp. 441 - 447
Copyright
Copyright © 2012 Australian Mathematical Publishing Association Inc. 

References

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