Omar Zai, Nur Athirah Farhana and Sarmin, Nor Haniza and Khasraw, Sanhan Muhammad Salih and Gambo, Ibrahim and Zaid, Nurhidayah (2023) The total non-zero divisor graph of some commutative rings. In: International Conference on Mathematics, Computational Sciences, and Statistics 2022, ICoMCoS 2022, 2 October 2022 - 3 October 2022, Surabaya, Indonesia - Hybrid, Surabaya.
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Official URL: http://dx.doi.org/10.1063/5.0181149
Abstract
In this study, we introduced a new concept of total non-zero divisor graph of a ring. The total non-zero divisor graph of a ring is defined as a simple undirected graph with its vertices are the non-zero elements of the ring and two distinct vertices are connected if and only if their product is not equal to zero, and their sum is in the its zero divisors sets. In this paper, the total non-zero divisor graph is constructed and the connectivity of the graph is explored. We prove that the total non-zero divisor graph is a null graph for the set of integers modulo p. The connectivity of the total non-zero divisor graph is also determined for the set of integers modulo n, where n ≠ p.
| Item Type: | Conference or Workshop Item (Paper) |
|---|---|
| Uncontrolled Keywords: | Ring theory, integers modulo. |
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Science |
| ID Code: | 107315 |
| Deposited By: | Muhamad Idham Sulong |
| Deposited On: | 01 Sep 2024 07:10 |
| Last Modified: | 01 Sep 2024 07:10 |
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