On G-locally primitive graphs of locally Twisted Wreath type and a conjecture of Weiss |
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Authors: | Pablo Spiga |
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Institution: | School of Mathematics and Statistics, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009 Perth, Australia |
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Abstract: | Let Γ be a connected G-vertex-transitive graph and let v be a vertex of Γ. The graph Γ is said to be G-locally primitive if the action of the vertex-stabiliser Gv on the neighbourhood Γ(v) of v is primitive. Furthermore, Γ is said to be of locally Twisted Wreath type if Gv is a primitive group of Twisted Wreath type in its action on Γ(v).Richard Weiss conjectured in 1978 that, there exists a function f:N→N such that if Γ is a connected G-vertex-transitive locally primitive graph of valency d and v is a vertex of Γ, then |Gv|?f(d). In this paper we prove this conjecture when Γ is of locally Twisted Wreath type. |
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Keywords: | Arc-transitive graph Primitive group Twisted Wreath Weiss Conjecture |
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