# On the intersection graph of a finite group

Hossein Shahsavari; Behrooz Khosravi

Czechoslovak Mathematical Journal (2017)

- Volume: 67, Issue: 4, page 1145-1153
- ISSN: 0011-4642

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topShahsavari, Hossein, and Khosravi, Behrooz. "On the intersection graph of a finite group." Czechoslovak Mathematical Journal 67.4 (2017): 1145-1153. <http://eudml.org/doc/294635>.

@article{Shahsavari2017,

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 $H\cap K\ne 1$. 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 $\{\rm Aut\}(\Gamma (G))$.},

author = {Shahsavari, Hossein, Khosravi, Behrooz},

journal = {Czechoslovak Mathematical Journal},

keywords = {intersection graph; regular graph; simple group; automorphism group},

language = {eng},

number = {4},

pages = {1145-1153},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {On the intersection graph of a finite group},

url = {http://eudml.org/doc/294635},

volume = {67},

year = {2017},

}

TY - JOUR

AU - Shahsavari, Hossein

AU - Khosravi, Behrooz

TI - On the intersection graph of a finite group

JO - Czechoslovak Mathematical Journal

PY - 2017

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 67

IS - 4

SP - 1145

EP - 1153

AB - 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 $H\cap K\ne 1$. 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 ${\rm Aut}(\Gamma (G))$.

LA - eng

KW - intersection graph; regular graph; simple group; automorphism group

UR - http://eudml.org/doc/294635

ER -

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