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quasiprimitive permutation groups

Proceedings of the Edinburgh Mathematical Society (1)

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On the Weiss conjecture for finite locally primitive graphs
Marston D. Conder, Cai Heng Li, Cheryl E. Praeger
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 43 / Issue 1 / February 2000

Published online by Cambridge University Press:

20 January 2009, pp. 129-138
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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.