Comments on the Clique Number of Zero-Divisor Graphs of Zn
In 2008, J. Skowronek-kazio´w extended the study of the clique number ωGZn to the zero-divisor graph of the ring Zn, but their result was imperfect. In this paper, we reconsider ωGZn of the ring Zn and give some counterexamples. We propose a constructive method for calculating ωGZn and give an algor...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/6591317 |
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| _version_ | 1849306065737351168 |
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| author | Yanzhao Tian Lixiang Li |
| author_facet | Yanzhao Tian Lixiang Li |
| author_sort | Yanzhao Tian |
| collection | DOAJ |
| description | In 2008, J. Skowronek-kazio´w extended the study of the clique number ωGZn to the zero-divisor graph of the ring Zn, but their result was imperfect. In this paper, we reconsider ωGZn of the ring Zn and give some counterexamples. We propose a constructive method for calculating ωGZn and give an algorithm for calculating the clique number of zero-divisor graph. Furthermore, we consider the case of the ternary zero-divisor and give the generation algorithm of the ternary zero-divisor graphs. |
| format | Article |
| id | doaj-art-341c61568c344bbda3e7bfa8d9a2d213 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-341c61568c344bbda3e7bfa8d9a2d2132025-08-20T03:55:12ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/6591317Comments on the Clique Number of Zero-Divisor Graphs of ZnYanzhao Tian0Lixiang Li1Information Security CenterInformation Security CenterIn 2008, J. Skowronek-kazio´w extended the study of the clique number ωGZn to the zero-divisor graph of the ring Zn, but their result was imperfect. In this paper, we reconsider ωGZn of the ring Zn and give some counterexamples. We propose a constructive method for calculating ωGZn and give an algorithm for calculating the clique number of zero-divisor graph. Furthermore, we consider the case of the ternary zero-divisor and give the generation algorithm of the ternary zero-divisor graphs.http://dx.doi.org/10.1155/2022/6591317 |
| spellingShingle | Yanzhao Tian Lixiang Li Comments on the Clique Number of Zero-Divisor Graphs of Zn Journal of Mathematics |
| title | Comments on the Clique Number of Zero-Divisor Graphs of Zn |
| title_full | Comments on the Clique Number of Zero-Divisor Graphs of Zn |
| title_fullStr | Comments on the Clique Number of Zero-Divisor Graphs of Zn |
| title_full_unstemmed | Comments on the Clique Number of Zero-Divisor Graphs of Zn |
| title_short | Comments on the Clique Number of Zero-Divisor Graphs of Zn |
| title_sort | comments on the clique number of zero divisor graphs of zn |
| url | http://dx.doi.org/10.1155/2022/6591317 |
| work_keys_str_mv | AT yanzhaotian commentsonthecliquenumberofzerodivisorgraphsofzn AT lixiangli commentsonthecliquenumberofzerodivisorgraphsofzn |