Non Deterministic Zero Divisor Graph

Abstract

A non-deterministic zero divisor graph refers to an element in a ring or algebraic structure that can multiply with another element to give zero, but the specific outcome of the multiplication is not uniquely determined. In other words, there may be multiple elements that can multiply with the given element to produce zero. This concept is typically encountered in non-commutative rings or algebras where the order of multiplication matters. In such structures, the existence of non-deterministic zero divisors can complicate calculations and lead to different results depending on the order of operations. In this paper, we examine that all the zerodivisor graphs are nondeterministic graph but the converse need not. We manifest the nondeterministic zero divisor graph is possible only with nonprimes. Hereby, we study about weighted graphs, Weiner index and golden ratio rule. Also we provide an algorithm for zero divisor graph of n parameters and thereby, explore the given graph is either deterministic or nondeterministic graph using python.