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 AG(R) with vertices Z(R)*, and two distinct vertices x and y are adjacent if and only if ann(xy)≠ann(x)∪ann(y). The notion of annihilator graph has...
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| Veröffentlicht in: | Algebra and Discrete Mathematics |
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| Datum: | 2017 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут прикладної математики і механіки НАН України
2017
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/156637 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | On the genus of the annhilator graph of a commutative ring / T.T. Chelvam, K. Selvakumar // Algebra and Discrete Mathematics. — 2017. — Vol. 24, № 2. — С. 191-208. — Бібліогр.: 26 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862531971123511296 |
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| author | Chelvam, T.T. Selvakumar, K. |
| author_facet | Chelvam, T.T. Selvakumar, K. |
| citation_txt | On the genus of the annhilator graph of a commutative ring / T.T. Chelvam, K. Selvakumar // Algebra and Discrete Mathematics. — 2017. — Vol. 24, № 2. — С. 191-208. — Бібліогр.: 26 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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 AG(R) with vertices Z(R)*, and two distinct vertices x and y are adjacent if and only if ann(xy)≠ann(x)∪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 AG(R) has genus less or equal to one
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| first_indexed | 2025-11-24T04:43:57Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-156637 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-11-24T04:43:57Z |
| publishDate | 2017 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Chelvam, T.T. Selvakumar, K. 2019-06-18T18:18:04Z 2019-06-18T18:18:04Z 2017 On the genus of the annhilator graph of a commutative ring / T.T. Chelvam, K. Selvakumar // Algebra and Discrete Mathematics. — 2017. — Vol. 24, № 2. — С. 191-208. — Бібліогр.: 26 назв. — англ. 1726-3255 2010 MSC:05C99, 05C15, 13A99. https://nasplib.isofts.kiev.ua/handle/123456789/156637 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 AG(R) with vertices Z(R)*, and two distinct vertices x and y are adjacent if and only if ann(xy)≠ann(x)∪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 AG(R) has genus less or equal to one This work was supported by the UGC-BSR One-time grant and UGC Major Research Project (F. No. 42-8/2013(SR)) of University Grants Commission, Government of India through first and second authors respectively. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics On the genus of the annhilator graph of a commutative ring Article published earlier |
| spellingShingle | On the genus of the annhilator graph of a commutative ring Chelvam, T.T. Selvakumar, K. |
| 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/156637 |
| work_keys_str_mv | AT chelvamtt onthegenusoftheannhilatorgraphofacommutativering AT selvakumark onthegenusoftheannhilatorgraphofacommutativering |