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On the Weiss conjecture for finite locally primitive graphs

  • Marston D. Conder (a1), Cai Heng Li (a2) and Cheryl E. Praeger (a2)

Abstract

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.

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References

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On the Weiss conjecture for finite locally primitive graphs

  • Marston D. Conder (a1), Cai Heng Li (a2) and Cheryl E. Praeger (a2)

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