The total non-zero divisor graph of some commutative rings.

• Main Authors: Omar Zai, Nur Athirah Farhana, Sarmin, Nor Haniza, Khasraw, Sanhan Muhammad Salih, Gambo, Ibrahim, Zaid, Nurhidayah
• Format: Conference or Workshop Item
• Published: 2023
• Subjects: QA Mathematics
• Online Access: http://eprints.utm.my/107315/; http://dx.doi.org/10.1063/5.0181149
• Institution: Universiti Teknologi Malaysia

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.