On the intersection graph of a finite group

Czechoslovak Mathematical Journal

Hossein Shahsavari, Behrooz Khosravi¹ 

关键词: intersection graph;    regular graph;    simple group;    automorphism group;   

DOI  :  10.21136/CMJ.2017.0446-16

学科分类：数学（综合）

来源: Akademie Ved Ceske Republiky

【 摘 要 】

  For a finite group $G$, the intersection graph of $G$ which is denoted by $\Gamma(G)$ is an undirected graph such that its vertices are all nontrivial proper subgroups of $G$ and two distinct vertices $H$ and $K$ are adjacent when $H\cap K\neq1$. In this paper we classify all finite groups whose intersection graphs are regular. Also, we find some results on the intersection graphs of simple groups and finally we study the structure of ${\rm Aut}(\Gamma(G))$.

【 授权许可】

Unknown