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Keywords:
intersection graph; leaf; nonsimple group; characterization
intersection graph; leaf; nonsimple group; characterization
Summary:
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.
References:
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