Czechoslovak Mathematical Journal

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.

Keywords: intersection graph; leaf; nonsimple group; characterization

Classification MSC: 05C25, 20D99

DOI: 10.21136/CMJ.2020.0250-19

PDF available at: Springer Institute of Mathematics CAS Digital Mathematics Library

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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: h.shahsavari13@yahoo.com, khosravibbb@yahoo.com

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