Year: 2012
Type: preprint
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 $|G_v|\leq c(L)$ holds. We show that an intransitive group is graph-restrictive if and only if it is semiregular.
Source: arXiv (Cornell University)
Authors: Spiga, Pablo, Verret, Gabriel
Institutions: University of Milano-Bicocca, University of Primorska
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2952655422