The intersection density of cubic arc-transitive graphs with $2$-arc-regular full automorphism group equal to $\operatorname{PGL}_2(q)$
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913753612681216 |
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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 |
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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 |