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On finite G-locally primitive graphs and the Weiss conjecture

Published online by Cambridge University Press:  17 April 2009

Mohammad A. Iranmanesh
Mohammad A. Iranmanesh
Affiliation:
Department of Mathematics, Yazd University, Yard, 89195–741Iran, e-mail: [email protected]
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A graph Γ is said to be a G-locally primitive graph, for G ≥ Aut Γ, if for every vertex, α, the stabiliser Gα induces a primitive permutation group on Γ (α) the set of vertices adjacent to α. In 1978 Richard Weiss conjectured that there exists a function f: ℕ →ℕ such that for any finite connected vertex-transitive G-locally primitive graph of valency d and a vertex α of the graph, |Gα| ≥ f(d). The purpose of this paper is to prove that, in the case Soc(G) = Sz(q), the conjecture is true.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 70 , Issue 3 , December 2004 , pp. 353 - 356
Copyright
Copyright © Australian Mathematical Society 2004

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