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

Abstract

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For a finite group G , the intersection graph of G which is denoted by Γ ( 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 ∩ K ≠ 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 Aut ( Γ ( G ) ) .

How to cite

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Shahsavari, 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 -

References

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