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. © 2011 Elsevier Inc.

Spiga, P. (2011). On G-locally primitive graphs of locally Twisted Wreath type and a conjecture of Weiss. JOURNAL OF COMBINATORIAL THEORY. SERIES A, 118(8), 2257-2260 [10.1016/j.jcta.2011.05.005].

On G-locally primitive graphs of locally Twisted Wreath type and a conjecture of Weiss

SPIGA, PABLO
2011

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. © 2011 Elsevier Inc.
Articolo in rivista - Articolo scientifico
Arc-transitive graph; Primitive group; Twisted wreath; Weiss conjecture; Discrete Mathematics and Combinatorics; Theoretical Computer Science; Computational Theory and Mathematics
English
2257
2260
4
Spiga, P. (2011). On G-locally primitive graphs of locally Twisted Wreath type and a conjecture of Weiss. JOURNAL OF COMBINATORIAL THEORY. SERIES A, 118(8), 2257-2260 [10.1016/j.jcta.2011.05.005].
Spiga, P
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/133188
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