The Non-Zero Divisor Graph of Prime Ring

Aliaa  Aqeel  Majeed; Ali Abd  Aubad; Smeer  Kadem

doi:10.24996/ijs.2025.66.7.%g

Authors

Aliaa Aqeel Majeed Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq https://orcid.org/0000-0001-9694-1021
Ali Abd Aubad Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq https://orcid.org/0000-0002-4764-2946
Smeer Kadem Department of Computer Techniques Engineering, Dijlah University College,Baghdad, Iraq

DOI:

https://doi.org/10.24996/ijs.2025.66.7.%25g

Keywords:

The non-zero divisor graph, prime ring, connected graph, girth

Abstract

uppose that be a ring, the non-zero divisor graph of denoted by and defined as a simple graph has vertex set \{0, and different vertices are adjacent if and only if or . For the prime ring R, we aim to investigate the structure of the graph . This involved the behavior of the nilpotent elements of the prime ring inside the graph as well as proving the graph is connected with girth of three. Furthermore, characterize certain universal vertex in the graph.