On intransitive graph-restrictive permutation groups

2012/11/14 by Spiga, Pablo, Verret, Gabriel · 1 citation
#05E18 #20B25 #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1211.3347

Abstract

Let Γ be a finite connected G-vertex-transitive graph and let v be a vertex of Γ. If the permutation group induced by the action of the vertex-stabiliser G_v on the neighbourhood Γ(v) is permutation isomorphic to L, then (Γ,G) is said to be locally-L. A permutation group L is graph-restrictive if there exists a constant c(L) such that, for every locally-L pair (Γ,G) and a vertex v of Γ, the inequality |G_v|≤ c(L) holds. We show that an intransitive group is graph-restrictive if and only if it is semiregular.

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