Some properties of various graphs associated with finite groups
In this paper we investigate some properties of the power graph and commuting graph associated with a finite group, using their tree-numbers. Among other things, it is shown that the simple group \(L_2(7)\) can be characterized through the tree-number of its power graph. Moreover, the classificati...
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| Дата: | 2021 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
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Lugansk National Taras Shevchenko University
2021
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1197 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-1197 |
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oai:ojs.admjournal.luguniv.edu.ua:article-11972021-07-19T08:39:30Z Some properties of various graphs associated with finite groups Chen, X. Y. Moghaddamfar, A. R. Zohourattar, M. power graph, commuting graph, tree-number, simple group 05C25, 20D05, 20D06 In this paper we investigate some properties of the power graph and commuting graph associated with a finite group, using their tree-numbers. Among other things, it is shown that the simple group \(L_2(7)\) can be characterized through the tree-number of its power graph. Moreover, the classification of groups with power-free decomposition is presented. Finally, we obtain an explicit formula concerning the tree-number of commuting graphs associated with the Suzuki simple groups. Lugansk National Taras Shevchenko University College of Sciences, Henan University of Technology, 450001, Zhengzhou, China 2021-07-19 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1197 10.12958/adm1197 Algebra and Discrete Mathematics; Vol 31, No 2 (2021) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1197/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/1197/375 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/1197/876 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/1197/877 Copyright (c) 2021 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| collection |
OJS |
| language |
English |
| topic |
power graph commuting graph tree-number simple group 05C25 20D05 20D06 |
| spellingShingle |
power graph commuting graph tree-number simple group 05C25 20D05 20D06 Chen, X. Y. Moghaddamfar, A. R. Zohourattar, M. Some properties of various graphs associated with finite groups |
| topic_facet |
power graph commuting graph tree-number simple group 05C25 20D05 20D06 |
| format |
Article |
| author |
Chen, X. Y. Moghaddamfar, A. R. Zohourattar, M. |
| author_facet |
Chen, X. Y. Moghaddamfar, A. R. Zohourattar, M. |
| author_sort |
Chen, X. Y. |
| title |
Some properties of various graphs associated with finite groups |
| title_short |
Some properties of various graphs associated with finite groups |
| title_full |
Some properties of various graphs associated with finite groups |
| title_fullStr |
Some properties of various graphs associated with finite groups |
| title_full_unstemmed |
Some properties of various graphs associated with finite groups |
| title_sort |
some properties of various graphs associated with finite groups |
| description |
In this paper we investigate some properties of the power graph and commuting graph associated with a finite group, using their tree-numbers. Among other things, it is shown that the simple group \(L_2(7)\) can be characterized through the tree-number of its power graph. Moreover, the classification of groups with power-free decomposition is presented. Finally, we obtain an explicit formula concerning the tree-number of commuting graphs associated with the Suzuki simple groups. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2021 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1197 |
| work_keys_str_mv |
AT chenxy somepropertiesofvariousgraphsassociatedwithfinitegroups AT moghaddamfarar somepropertiesofvariousgraphsassociatedwithfinitegroups AT zohourattarm somepropertiesofvariousgraphsassociatedwithfinitegroups |
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2024-04-12T06:27:21Z |
| last_indexed |
2024-04-12T06:27:21Z |
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1796109245441114112 |