On graph-restrictive permutation groups

Authors:
Primo Potočnik;Pablo Spiga;Gabriel Verret
Affiliations:
Institute of Mathematics, Physics, and Mechanics, Jadranska 19, 1000 Ljubljana, Slovenia;School of Mathematics and Statistics, The University of Western Australia, Crawley, WA 6009, Australia;Institute of Mathematics, Physics, and Mechanics, Jadranska 19, 1000 Ljubljana, Slovenia
Venue:
Journal of Combinatorial Theory Series B
Year:
2012

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Abstract

Let @C be a connected G-vertex-transitive graph, let v be a vertex of @C and let L=G"v^@C^(^v^) be the permutation group induced by the action of the vertex-stabiliser G"v on the neighbourhood @C(v). Then (@C,G) is said to be locally-L. A transitive permutation group L is graph-restrictive if there exists a constant c(L) such that, for every locally-L pair (@C,G) and an arc (u,v) of @C, the inequality |G"u"v|=