Czechoslovak Mathematical Journal, Vol. 71, No. 1, pp. 191-209, 2021
Characterization by intersection graph of some families of finite nonsimple groups
Hossein Shahsavari, Behrooz Khosravi
Received June 3, 2019. Published online September 17, 2020.
Abstract: 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 $H\cap K\neq1$. 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.
Affiliations: Hossein Shahsavari, Behrooz Khosravi (corresponding author), Department of Pure Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), 424 Hafez Avenue, Tehran 15914, Iran, e-mail: firstname.lastname@example.org, email@example.com