On the genus of the annhilator graph of a commutative ring
Let \(R\) be a commutative ring and \(Z(R)^*\) be its set of non-zero zero-divisors. The annihilator graph of a commutative ring \(R\) is the simple undirected graph \(\operatorname{AG}(R)\) with vertices \(Z(R)^*\), and two distinct vertices \(x\) and \(y\) are adjacent if and only if \(\operatorna...
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| Datum: | 2018 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Lugansk National Taras Shevchenko University
2018
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| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/79 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543071708119040 |
|---|---|
| author | Tamizh Chelvam, T. Selvakumar, K. |
| author_facet | Tamizh Chelvam, T. Selvakumar, K. |
| author_sort | Tamizh Chelvam, T. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-04-26T02:43:18Z |
| description | Let \(R\) be a commutative ring and \(Z(R)^*\) be its set of non-zero zero-divisors. The annihilator graph of a commutative ring \(R\) is the simple undirected graph \(\operatorname{AG}(R)\) with vertices \(Z(R)^*\), and two distinct vertices \(x\) and \(y\) are adjacent if and only if \(\operatorname{ann}(xy)\neq \operatorname{ann}(x)\cup \operatorname{ann}(y)\). The notion of annihilator graph has been introduced and studied by A. Badawi [7]. In this paper, we determine isomorphism classes of finite commutative rings with identity whose \(\operatorname{AG}(R)\) has genus less or equal to one. |
| first_indexed | 2025-12-02T15:32:40Z |
| format | Article |
| id | admjournalluguniveduua-article-79 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:32:40Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-792018-04-26T02:43:18Z On the genus of the annhilator graph of a commutative ring Tamizh Chelvam, T. Selvakumar, K. commutative ring, annihilator graph, genus, planar, local rings 05C99, 05C15, 13A99 Let \(R\) be a commutative ring and \(Z(R)^*\) be its set of non-zero zero-divisors. The annihilator graph of a commutative ring \(R\) is the simple undirected graph \(\operatorname{AG}(R)\) with vertices \(Z(R)^*\), and two distinct vertices \(x\) and \(y\) are adjacent if and only if \(\operatorname{ann}(xy)\neq \operatorname{ann}(x)\cup \operatorname{ann}(y)\). The notion of annihilator graph has been introduced and studied by A. Badawi [7]. In this paper, we determine isomorphism classes of finite commutative rings with identity whose \(\operatorname{AG}(R)\) has genus less or equal to one. Lugansk National Taras Shevchenko University 2018-01-24 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/79 Algebra and Discrete Mathematics; Vol 24, No 2 (2017) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/79/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/79/56 Copyright (c) 2018 Algebra and Discrete Mathematics |
| spellingShingle | commutative ring annihilator graph genus planar local rings 05C99 05C15 13A99 Tamizh Chelvam, T. Selvakumar, K. On the genus of the annhilator graph of a commutative ring |
| title | On the genus of the annhilator graph of a commutative ring |
| title_full | On the genus of the annhilator graph of a commutative ring |
| title_fullStr | On the genus of the annhilator graph of a commutative ring |
| title_full_unstemmed | On the genus of the annhilator graph of a commutative ring |
| title_short | On the genus of the annhilator graph of a commutative ring |
| title_sort | on the genus of the annhilator graph of a commutative ring |
| topic | commutative ring annihilator graph genus planar local rings 05C99 05C15 13A99 |
| topic_facet | commutative ring annihilator graph genus planar local rings 05C99 05C15 13A99 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/79 |
| work_keys_str_mv | AT tamizhchelvamt onthegenusoftheannhilatorgraphofacommutativering AT selvakumark onthegenusoftheannhilatorgraphofacommutativering |