The edge chromatic number of \(\Gamma_{I}(R)\)
For a commutative ring \(R\) and an ideal \(I\) of \(R\), the ideal-based zero-divisor graph is the undirected graph \(\Gamma_{I}(R)\) with vertices \(\{x\in R-I: xy\in I~ \text{for some}~ y\in R-I\}\), where distinct vertices \(x\) and \(y\) are adjacent if and only if \(xy\in I\). In this paper, w...
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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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| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/76 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| _version_ | 1856543360415694849 |
|---|---|
| author | Kala, R. Mallika, A. Selvakumar, K. |
| author_facet | Kala, R. Mallika, A. Selvakumar, K. |
| author_sort | Kala, R. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-04-26T02:43:18Z |
| description | For a commutative ring \(R\) and an ideal \(I\) of \(R\), the ideal-based zero-divisor graph is the undirected graph \(\Gamma_{I}(R)\) with vertices \(\{x\in R-I: xy\in I~ \text{for some}~ y\in R-I\}\), where distinct vertices \(x\) and \(y\) are adjacent if and only if \(xy\in I\). In this paper, we discuss the nature of the edges of \(\Gamma_{I}(R)\). We also find the edge chromatic number for the graph \(\Gamma_{I}(R)\). |
| first_indexed | 2026-02-08T07:58:03Z |
| format | Article |
| id | admjournalluguniveduua-article-76 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2026-02-08T07:58:03Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-762018-04-26T02:43:18Z The edge chromatic number of \(\Gamma_{I}(R)\) Kala, R. Mallika, A. Selvakumar, K. zero-divisor graph, chromatic number, ideal-based zero-divisor graph 05C99, 13A15, 13F10 For a commutative ring \(R\) and an ideal \(I\) of \(R\), the ideal-based zero-divisor graph is the undirected graph \(\Gamma_{I}(R)\) with vertices \(\{x\in R-I: xy\in I~ \text{for some}~ y\in R-I\}\), where distinct vertices \(x\) and \(y\) are adjacent if and only if \(xy\in I\). In this paper, we discuss the nature of the edges of \(\Gamma_{I}(R)\). We also find the edge chromatic number for the graph \(\Gamma_{I}(R)\). Lugansk National Taras Shevchenko University DST-INSPIRE Fellowship 2018-01-24 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/76 Algebra and Discrete Mathematics; Vol 24, No 2 (2017) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/76/pdf Copyright (c) 2018 Algebra and Discrete Mathematics |
| spellingShingle | zero-divisor graph chromatic number ideal-based zero-divisor graph 05C99 13A15 13F10 Kala, R. Mallika, A. Selvakumar, K. The edge chromatic number of \(\Gamma_{I}(R)\) |
| title | The edge chromatic number of \(\Gamma_{I}(R)\) |
| title_full | The edge chromatic number of \(\Gamma_{I}(R)\) |
| title_fullStr | The edge chromatic number of \(\Gamma_{I}(R)\) |
| title_full_unstemmed | The edge chromatic number of \(\Gamma_{I}(R)\) |
| title_short | The edge chromatic number of \(\Gamma_{I}(R)\) |
| title_sort | edge chromatic number of \(\gamma_{i}(r)\) |
| topic | zero-divisor graph chromatic number ideal-based zero-divisor graph 05C99 13A15 13F10 |
| topic_facet | zero-divisor graph chromatic number ideal-based zero-divisor graph 05C99 13A15 13F10 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/76 |
| work_keys_str_mv | AT kalar theedgechromaticnumberofgammair AT mallikaa theedgechromaticnumberofgammair AT selvakumark theedgechromaticnumberofgammair AT kalar edgechromaticnumberofgammair AT mallikaa edgechromaticnumberofgammair AT selvakumark edgechromaticnumberofgammair |