On the non-zero divisor graphs of some finite commutative rings
The study of rings and graphs has been explored extensively by researchers. To gain a more effective understanding on the concepts of the rings and graphs, more researches on graphs of different types of rings are required. This manuscript provides a different study on the concepts of commutative ri...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Universiti Putra Malaysia
2023
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| Online Access: | http://eprints.utm.my/105396/1/NorHanizaSarmin2023_OntheNonZeroDivisorGraphsofSome.pdf |
| _version_ | 1811132121721339904 |
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| author | Omar Zai, Nur Athirah Farhana Sarmin, Nor Haniza Khasraw, Sanhan Muhammad Salih Gambo, Ibrahim Zaid, Nurhidayah |
| author_facet | Omar Zai, Nur Athirah Farhana Sarmin, Nor Haniza Khasraw, Sanhan Muhammad Salih Gambo, Ibrahim Zaid, Nurhidayah |
| author_sort | Omar Zai, Nur Athirah Farhana |
| collection | ePrints |
| description | The study of rings and graphs has been explored extensively by researchers. To gain a more effective understanding on the concepts of the rings and graphs, more researches on graphs of different types of rings are required. This manuscript provides a different study on the concepts of commutative rings and undirected graphs. The non-zero divisor graph, Γ(R) of a ring R is a simple undirected graph in which its set of vertices consists of all non-zero elements of R and two different vertices are joint by an edge if their product is not equal to zero. In this paper, the commutative rings are the ring of integers modulo n where n = 8k and k ≤ 3. The zero divisors are found first using the definition and then the non-zero divisor graphs are constructed. The manuscript explores some properties of non-zero divisor graph such as the chromatic number and the clique number. The result has shown that Γ(Z8k) is perfect. |
| first_indexed | 2024-09-23T23:57:16Z |
| format | Article |
| id | utm.eprints-105396 |
| institution | Universiti Teknologi Malaysia - ePrints |
| language | English |
| last_indexed | 2024-09-23T23:57:16Z |
| publishDate | 2023 |
| publisher | Universiti Putra Malaysia |
| record_format | dspace |
| spelling | utm.eprints-1053962024-04-24T06:51:07Z http://eprints.utm.my/105396/ On the non-zero divisor graphs of some finite commutative rings Omar Zai, Nur Athirah Farhana Sarmin, Nor Haniza Khasraw, Sanhan Muhammad Salih Gambo, Ibrahim Zaid, Nurhidayah QA Mathematics The study of rings and graphs has been explored extensively by researchers. To gain a more effective understanding on the concepts of the rings and graphs, more researches on graphs of different types of rings are required. This manuscript provides a different study on the concepts of commutative rings and undirected graphs. The non-zero divisor graph, Γ(R) of a ring R is a simple undirected graph in which its set of vertices consists of all non-zero elements of R and two different vertices are joint by an edge if their product is not equal to zero. In this paper, the commutative rings are the ring of integers modulo n where n = 8k and k ≤ 3. The zero divisors are found first using the definition and then the non-zero divisor graphs are constructed. The manuscript explores some properties of non-zero divisor graph such as the chromatic number and the clique number. The result has shown that Γ(Z8k) is perfect. Universiti Putra Malaysia 2023 Article PeerReviewed application/pdf en http://eprints.utm.my/105396/1/NorHanizaSarmin2023_OntheNonZeroDivisorGraphsofSome.pdf Omar Zai, Nur Athirah Farhana and Sarmin, Nor Haniza and Khasraw, Sanhan Muhammad Salih and Gambo, Ibrahim and Zaid, Nurhidayah (2023) On the non-zero divisor graphs of some finite commutative rings. Malaysian Journal of Mathematical Sciences, 17 (2). pp. 105-112. ISSN 1823-8343 http://dx.doi.org/10.47836/mjms.17.2.02 DOI:10.47836/mjms.17.2.02 |
| spellingShingle | QA Mathematics Omar Zai, Nur Athirah Farhana Sarmin, Nor Haniza Khasraw, Sanhan Muhammad Salih Gambo, Ibrahim Zaid, Nurhidayah On the non-zero divisor graphs of some finite commutative rings |
| title | On the non-zero divisor graphs of some finite commutative rings |
| title_full | On the non-zero divisor graphs of some finite commutative rings |
| title_fullStr | On the non-zero divisor graphs of some finite commutative rings |
| title_full_unstemmed | On the non-zero divisor graphs of some finite commutative rings |
| title_short | On the non-zero divisor graphs of some finite commutative rings |
| title_sort | on the non zero divisor graphs of some finite commutative rings |
| topic | QA Mathematics |
| url | http://eprints.utm.my/105396/1/NorHanizaSarmin2023_OntheNonZeroDivisorGraphsofSome.pdf |
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