Probabilistic characterizations of some finite ring of matrices and its zero divisor graph

Abstract

Let R be a finite ring. In this study, the probability that two random elements chosen from a finite ring have product zero is determined for some finite ring of matrices over Zn. Then, the results are used to construct the zero divisor graph which is defined as a graph whose vertices are the nonzero zero divisors of R and two distinct vertices x and y are adjacent if and only if xy = 0.