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On the Weiss conjecture for finite locally primitive graphs

Published online by Cambridge University Press:  20 January 2009

Marston D. Conder ,
Cai Heng Li  and
Cheryl E. Praeger
Marston D. Conder
Affiliation:
Department of Mathematics, University of Auckland, Auckland, New Zealand
Cai Heng Li
Affiliation:
Department of Mathematics, University of Western Australia, Nedlands, WA 6907, Australia
Cheryl E. Praeger
Affiliation:
Department of Mathematics, University of Western Australia, Nedlands, WA 6907, Australia
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Abstract

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A graph Γ is said to be locally primitive if, for each vertex α, the stabilizer in Aut Γ of α induces a primitive permutation group on the set of vertices adjacent to α. In 1978, Richard Weiss conjectured that for a finite vertex-transitive locally primitive graph Γ, the number of automorphisms fixing a given vertex is bounded above by some function of the valency of Γ. In this paper we prove that the conjecture is true for finite non-bipartite graphsprovided that it is true in the case in which Aut Γ contains a locally primitive subgroup that is almost simple.

Keywords

vertex-transitive graphslocally primitive graphsquasiprimitive permutation groupsalmost simple groups
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 43 , Issue 1 , February 2000 , pp. 129 - 138
Copyright
Copyright © Edinburgh Mathematical Society 2000

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