Geodesic
On intransitive graph-restrictive permutation groups
Journal of Algebraic Combinatorics, Tome 40 (2014) no. 1, pp. 179-185.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Let $\Gamma$ be a finite connected $G$-vertex-transitive graph and let $v$ be a vertex of $\Gamma$. If the permutation group induced by the action of the vertex-stabiliser $G_v$ on the neighbourhood $\Gamma (v)$ is permutation isomorphic to $L$, then $(\Gamma ,G)$ 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 $(\Gamma ,G)$ and a vertex $v$ of $\Gamma$, the inequality $\vert G_v\vert\leq c(L)$ holds. We show that an intransitive group is graph-restrictive if and only if it is semiregular.
Classification : 05E18, 20B25
Keywords: permutation group, semi-regular permutation group, vertex-transitive graph, graph-restrictive permutation group 
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Spiga, Pablo; Verret, Gabriel. On intransitive graph-restrictive permutation groups. Journal of Algebraic Combinatorics, Tome 40 (2014) no. 1, pp. 179-185. http://geodesic.mathdoc.fr/item/JAC_2014__40_1_a6/