Power graph of finite abelian groups
Let \(G\) be a group. The power graph \(\Gamma_P(G)\) of \(G\) is a graph with vertex set \(V(\Gamma_P(G)) = G\) and two distinct vertices \(x\) and \(y\) are adjacent in \(\Gamma_P(G)\) if and only if either \(x^i=y\) or \(y^j=x\), where \(2\leq i,j \leq n\). In this paper, we obtain some fundament...
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| Дата: | 2018 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2018
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/753 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| _version_ | 1856543360537329664 |
|---|---|
| author | Chelvam, T. Tamizh Sattanathan, M. |
| author_facet | Chelvam, T. Tamizh Sattanathan, M. |
| author_sort | Chelvam, T. Tamizh |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-04-26T01:26:05Z |
| description | Let \(G\) be a group. The power graph \(\Gamma_P(G)\) of \(G\) is a graph with vertex set \(V(\Gamma_P(G)) = G\) and two distinct vertices \(x\) and \(y\) are adjacent in \(\Gamma_P(G)\) if and only if either \(x^i=y\) or \(y^j=x\), where \(2\leq i,j \leq n\). In this paper, we obtain some fundamental characterizations of the power graph. Also, we characterize certain classes of power graphs of finite abelian groups. |
| first_indexed | 2026-02-08T07:58:02Z |
| format | Article |
| id | admjournalluguniveduua-article-753 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2026-02-08T07:58:02Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-7532018-04-26T01:26:05Z Power graph of finite abelian groups Chelvam, T. Tamizh Sattanathan, M. power graph, planar graph, Eulerian graph, finite group 05C25 Let \(G\) be a group. The power graph \(\Gamma_P(G)\) of \(G\) is a graph with vertex set \(V(\Gamma_P(G)) = G\) and two distinct vertices \(x\) and \(y\) are adjacent in \(\Gamma_P(G)\) if and only if either \(x^i=y\) or \(y^j=x\), where \(2\leq i,j \leq n\). In this paper, we obtain some fundamental characterizations of the power graph. Also, we characterize certain classes of power graphs of finite abelian groups. Lugansk National Taras Shevchenko University 2018-04-26 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/753 Algebra and Discrete Mathematics; Vol 16, No 1 (2013) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/753/282 Copyright (c) 2018 Algebra and Discrete Mathematics |
| spellingShingle | power graph planar graph Eulerian graph finite group 05C25 Chelvam, T. Tamizh Sattanathan, M. Power graph of finite abelian groups |
| title | Power graph of finite abelian groups |
| title_full | Power graph of finite abelian groups |
| title_fullStr | Power graph of finite abelian groups |
| title_full_unstemmed | Power graph of finite abelian groups |
| title_short | Power graph of finite abelian groups |
| title_sort | power graph of finite abelian groups |
| topic | power graph planar graph Eulerian graph finite group 05C25 |
| topic_facet | power graph planar graph Eulerian graph finite group 05C25 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/753 |
| work_keys_str_mv | AT chelvamttamizh powergraphoffiniteabeliangroups AT sattanathanm powergraphoffiniteabeliangroups |