On finite G-locally primitive graphs and the Weiss conjecture

Publisher： Cambridge University Press

E-ISSN： 1755-1633|70|3|353-356

ISSN： 0004-9727

Source： Bulletin of the Australian Mathematical Society, Vol.70, Iss.3, 2004-12, pp. : 353-356

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Abstract

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: → 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.

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