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

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240kB |

Official URL: http://dx.doi.org/10.47836/mjms.17.2.02

## Abstract

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.

Item Type: | Article |
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Uncontrolled Keywords: | commutative rings, non-zero divisor graphs, ring, zero divisors |

Subjects: | Q Science > QA Mathematics |

Divisions: | Science |

ID Code: | 105396 |

Deposited By: | Yanti Mohd Shah |

Deposited On: | 24 Apr 2024 06:51 |

Last Modified: | 24 Apr 2024 06:51 |

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