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Characterization by intersection graph of some families of finite nonsimple groups
Czechoslovak Mathematical Journal, Tome 71 (2021) no. 1, pp. 191-209
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For a finite group $G$, $\Gamma (G)$, the intersection graph of $G$, is a simple graph whose vertices are all nontrivial proper subgroups of $G$ and two distinct vertices $H$ and $K$ are adjacent when $H\cap K\neq 1$. In this paper, we classify all finite nonsimple groups whose intersection graphs have a leaf and also we discuss the characterizability of them using their intersection graphs.
For a finite group $G$, $\Gamma (G)$, the intersection graph of $G$, is a simple graph whose vertices are all nontrivial proper subgroups of $G$ and two distinct vertices $H$ and $K$ are adjacent when $H\cap K\neq 1$. In this paper, we classify all finite nonsimple groups whose intersection graphs have a leaf and also we discuss the characterizability of them using their intersection graphs.
DOI : 10.21136/CMJ.2020.0250-19
Classification : 05C25, 20D99
Keywords: intersection graph; leaf; nonsimple group; characterization 
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Shahsavari, Hossein; Khosravi, Behrooz. Characterization by intersection graph of some families of finite nonsimple groups. Czechoslovak Mathematical Journal, Tome 71 (2021) no. 1, pp. 191-209. doi: 10.21136/CMJ.2020.0250-19

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