Thickness of the subgroup intersection graph of a finite group

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 thic...

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Bibliographic Details
Published inAIMS mathematics Vol. 6; no. 3; pp. 2590 - 2606
Main Authors Su, Huadong, Zhu, Ling
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2021
Subjects
finite group
outerthickness
subgroup intersection graph
thickness
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Summary: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.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2021157