Let p be a prime and let L be either the intransitive permutation group Cp×Cp of degree 2p or the transitive permutation group CpwrC2 of degree 2p. Let Γ be a connected G-vertex-transitive and G-edge-transitive graph and let v be a vertex of Γ. We show that if the permutation group induced by the vertex-stabiliser Gv on the neighbourhood Γ(v) is isomorphic to L then either |V(Γ)|≥p|Gv|logp(|Gv|/2), or |V(Γ)| is bounded by a constant depending only on p, or Γ is a very-well understood graph. This generalises a few recent results.

Spiga, P., Verret, G. (2016). On the order of vertex-stabilisers in vertex-transitive graphs with local group Cp×Cp or CpwrC2. JOURNAL OF ALGEBRA, 448, 174-209 [10.1016/j.jalgebra.2015.09.033].

On the order of vertex-stabilisers in vertex-transitive graphs with local group Cp×Cp or CpwrC2

SPIGA, PABLO
Primo
;
2016

Abstract

Let p be a prime and let L be either the intransitive permutation group Cp×Cp of degree 2p or the transitive permutation group CpwrC2 of degree 2p. Let Γ be a connected G-vertex-transitive and G-edge-transitive graph and let v be a vertex of Γ. We show that if the permutation group induced by the vertex-stabiliser Gv on the neighbourhood Γ(v) is isomorphic to L then either |V(Γ)|≥p|Gv|logp(|Gv|/2), or |V(Γ)| is bounded by a constant depending only on p, or Γ is a very-well understood graph. This generalises a few recent results.
Articolo in rivista - Articolo scientifico
Arc-transitive; Edge-transitive; Graph; Half-arc-transitive; Vertex-stabiliser; Vertex-transitive;
Arc-transitive; Edge-transitive; Graph; Half-arc-transitive; Vertex-stabiliser; Vertex-transitive
English
2016
448
174
209
none
Spiga, P., Verret, G. (2016). On the order of vertex-stabilisers in vertex-transitive graphs with local group Cp×Cp or CpwrC2. JOURNAL OF ALGEBRA, 448, 174-209 [10.1016/j.jalgebra.2015.09.033].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/99625
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