Czechoslovak Mathematical Journal, Vol. 67, No. 4, pp. 1145-1153, 2017

On the intersection graph of a finite group

Hossein Shahsavari, Behrooz Khosravi

Received August 20, 2016.   First published October 18, 2017.

Abstract:  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 ${\rm Aut}(\Gamma(G))$.
Keywords:  intersection graph; regular graph; simple group; automorphism group
Classification MSC:  05C25, 20E32
DOI:  10.21136/CMJ.2017.0446-16

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Affiliations:   Hossein Shahsavari, Behrooz Khosravi, Department of Pure Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), 424 Hafez Ave., Tehran 15914, Iran, e-mail:,

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