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双传递二图的切换类中的顶点传递强正则图

Vertex-transitive strongly regular graphs in the switching class of doubly transitive two-graphs

Robert F. Bailey, Gábor P. Nagy, Valentino Smaldore

arXiv 2608.30330首次发表:更新:

发表机构

Memorial University–Grenfell Campus; University of Szeged; Università degli Studi di Padova(纪念大学格伦费尔分校; 塞格德大学; 帕多瓦大学)

机构由 AI 辅助整理,请以论文原文为准。

AI 中文总结

本文对关联二图源于PΣL(2,q)的顶点传递强正则图进行分类,得到了一类新的此类图族。

AI 中文摘要

设G是在有限集V上2-传递作用的置换群,𝒯=(V,T)是自同构群包含G的二图。本文对顶点集为V、自同构群为G的传递极大子群且关联二图为𝒯的强正则图Γ进行分类,得到了一类关联二图源于PΣL(2,q)的新型顶点传递强正则图。

英文摘要

Let $G$ be a permutation group that acts $2$-transitively on the finite set $V$ and let $\mathcal{T}=(V,T)$ be a two-graph whose automorphism group contains $G$. In this paper, we classify those strongly regular graphs $Γ$ with vertex set $V$ whose automorphism group is a transitive maximal subgroup of $G$ and whose associated two-graph is $\mathcal{T}$. In doing so, we obtain a new family of vertex-transitive strongly regular graphs whose associated two-graph arises from $PΣL(2,q)$.

论文原文

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