Double-toroidal and \(1\)-planar non-commuting graph of a group
Let \(G\) be a finite non-abelian group and denote by \(Z(G)\) its center. The non-commuting graph of \(G\) on a transversal of the center is the graph whose vertices are the non-central elements of a transversal of \(Z(G)\) in \(G\) and two vertices \(x\) and \(y\) are adjacent whenever \(xy\neq yx...
Збережено в:
| Дата: | 2023 |
|---|---|
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2023
|
| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1935 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| _version_ | 1856543246134542336 |
|---|---|
| author | Pezzott, J. C. M. |
| author_facet | Pezzott, J. C. M. |
| author_sort | Pezzott, J. C. M. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2023-02-08T16:55:57Z |
| description | Let \(G\) be a finite non-abelian group and denote by \(Z(G)\) its center. The non-commuting graph of \(G\) on a transversal of the center is the graph whose vertices are the non-central elements of a transversal of \(Z(G)\) in \(G\) and two vertices \(x\) and \(y\) are adjacent whenever \(xy\neq yx\). In this work, we classify the finite non-abelian groups whose non-commuting graph on a transversal of the center is double-toroidal or \(1\)-planar. |
| first_indexed | 2025-12-02T15:30:41Z |
| format | Article |
| id | admjournalluguniveduua-article-1935 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:30:41Z |
| publishDate | 2023 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-19352023-02-08T16:55:57Z Double-toroidal and \(1\)-planar non-commuting graph of a group Pezzott, J. C. M. non-commuting graph, double-toroidal graph, \(1\)-planar graph, isoclinism 05C25, 05C10 Let \(G\) be a finite non-abelian group and denote by \(Z(G)\) its center. The non-commuting graph of \(G\) on a transversal of the center is the graph whose vertices are the non-central elements of a transversal of \(Z(G)\) in \(G\) and two vertices \(x\) and \(y\) are adjacent whenever \(xy\neq yx\). In this work, we classify the finite non-abelian groups whose non-commuting graph on a transversal of the center is double-toroidal or \(1\)-planar. Lugansk National Taras Shevchenko University 2023-02-08 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1935 10.12958/adm1935 Algebra and Discrete Mathematics; Vol 34, No 1 (2022) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1935/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/1935/958 Copyright (c) 2023 Algebra and Discrete Mathematics |
| spellingShingle | non-commuting graph double-toroidal graph \(1\)-planar graph isoclinism 05C25 05C10 Pezzott, J. C. M. Double-toroidal and \(1\)-planar non-commuting graph of a group |
| title | Double-toroidal and \(1\)-planar non-commuting graph of a group |
| title_full | Double-toroidal and \(1\)-planar non-commuting graph of a group |
| title_fullStr | Double-toroidal and \(1\)-planar non-commuting graph of a group |
| title_full_unstemmed | Double-toroidal and \(1\)-planar non-commuting graph of a group |
| title_short | Double-toroidal and \(1\)-planar non-commuting graph of a group |
| title_sort | double-toroidal and \(1\)-planar non-commuting graph of a group |
| topic | non-commuting graph double-toroidal graph \(1\)-planar graph isoclinism 05C25 05C10 |
| topic_facet | non-commuting graph double-toroidal graph \(1\)-planar graph isoclinism 05C25 05C10 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1935 |
| work_keys_str_mv | AT pezzottjcm doubletoroidaland1planarnoncommutinggraphofagroup |