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...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Universiti Putra Malaysia
2023
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| Subjects: | |
| Online Access: | http://eprints.utm.my/105396/1/NorHanizaSarmin2023_OntheNonZeroDivisorGraphsofSome.pdf http://eprints.utm.my/105396/ http://dx.doi.org/10.47836/mjms.17.2.02 |
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| Institution: | Universiti Teknologi Malaysia |
| Language: | English |
| Summary: | 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. |
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