The Non-Zero Divisor Graph of Prime Ring

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.