Thickness of the subgroup intersection graph of a finite group

Huadong Su; Ling Zhu; Huadong Su; Ling Zhu

doi:10.3934/math.2021157

AIMS Mathematics

2021, Volume 6, Issue 3: 2590-2606. doi: 10.3934/math.2021157

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Research article

Thickness of the subgroup intersection graph of a finite group

Huadong Su ^{1
,
,},
Ling Zhu ²

1.
School of Science, Beibu Gulf University, Qinzhou, Guangxi, 535011, P. R. China
2.
School of Artificial Intelligence, Jiangxi University of Applied Science, Nanchang, Jiangxi, 330100, P.R, China

Received: 11 September 2020 Accepted: 21 December 2020 Published: 25 December 2020
MSC : 05C25, 05C10, 20D60

Let $ G $ be a finite group. The intersection graph of subgroups of $ G $ is a graph whose vertices are all non-trivial subgroups of $ G $ and in which two distinct vertices $ H $ and $ K $ are adjacent if and only if $ H\cap K\neq 1 $. In this paper, we classify all finite abelian groups whose thickness and outerthickness of subgroup intersection graphs are 1 and 2, respectively. We also investigate the thickness and outerthickness of subgroup intersection graphs for some finite non-abelian groups.
- thickness,
- outerthickness,
- subgroup intersection graph,
- finite group
Citation: Huadong Su, Ling Zhu. Thickness of the subgroup intersection graph of a finite group[J]. AIMS Mathematics, 2021, 6(3): 2590-2606. doi: 10.3934/math.2021157

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Abstract

Let $ G $ be a finite group. The intersection graph of subgroups of $ G $ is a graph whose vertices are all non-trivial subgroups of $ G $ and in which two distinct vertices $ H $ and $ K $ are adjacent if and only if $ H\cap K\neq 1 $. In this paper, we classify all finite abelian groups whose thickness and outerthickness of subgroup intersection graphs are 1 and 2, respectively. We also investigate the thickness and outerthickness of subgroup intersection graphs for some finite non-abelian groups.

References

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