The intersection density of cubic arc-transitive graphs with $2$-arc-regular full automorphism group equal to $\operatorname{PGL}_2(q)$

Fuente: arXiv
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Main Authors: Meagher, Karen, Razafimahatratra, Andriaherimanana Sarobidy
Format: Preprint
Published: 2025
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author Meagher, Karen
Razafimahatratra, Andriaherimanana Sarobidy
author_facet Meagher, Karen
Razafimahatratra, Andriaherimanana Sarobidy
contents The \emph{intersection density} of a transitive permutation group $G\leq \operatorname{Sym}(Ω)$ is the ratio between the largest size of a subset of $G$ in which any two agree on at least one element of $Ω$, and the order of a point-stabilizer of $G$. In this paper, we determine the intersection densities of the automorphism group of the arc-transitive graphs admitting a $2$-arc-regular full automorphism group $G^* = \operatorname{PGL}_2(q)$ and an arc-regular subgroup of automorphism $G = \operatorname{PSL}_2(q)$.
format Preprint
id arxiv_https___arxiv_org_abs_2503_17769
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle The intersection density of cubic arc-transitive graphs with $2$-arc-regular full automorphism group equal to $\operatorname{PGL}_2(q)$
Meagher, Karen
Razafimahatratra, Andriaherimanana Sarobidy
Combinatorics
Primary 05C35, Secondary 05C69, 20B05
The \emph{intersection density} of a transitive permutation group $G\leq \operatorname{Sym}(Ω)$ is the ratio between the largest size of a subset of $G$ in which any two agree on at least one element of $Ω$, and the order of a point-stabilizer of $G$. In this paper, we determine the intersection densities of the automorphism group of the arc-transitive graphs admitting a $2$-arc-regular full automorphism group $G^* = \operatorname{PGL}_2(q)$ and an arc-regular subgroup of automorphism $G = \operatorname{PSL}_2(q)$.
title The intersection density of cubic arc-transitive graphs with $2$-arc-regular full automorphism group equal to $\operatorname{PGL}_2(q)$
topic Combinatorics
Primary 05C35, Secondary 05C69, 20B05
url https://arxiv.org/abs/2503.17769