Raden Muhammad Kevin Ardiansyah, Mohammad Agung
Assume R is a commutativeringwith unity and RM denote a module overi? or i?-module. The set of zero divisors of RM denoted by Z{RM) and the zero divisor graph of RM denoted by T(RM). The vertices of T(RM) consist of all non-zero zero divisors of RM, denoted as Z\RM) = Z(RM)\{0}, where two distinct vertices x,y e Z\RM) adjacent if and only if x e Ann(y)M ory e Ann(x)M, for Ann(pi) = {r e R | rm = OM}- The graph-approach to algebraic structures has been a popular research topic for more than twenty years, one of which is the zero divisor graph of rings. However, the concept of zero divisor graph has not been widely applied to modules. The purpose of this research is to represent the graph of zero divisor element of zZp2 and zZp3, in other words, to find the general form of T(zZp2) and T(zZp3). The reasearch found that the general form of T(zZp2) is Kp.\ (complete graph withp-\ vertices) andT(zZp3) is Kp.\ I) XP(P.\)(XP(P.\) denote p(p-l) vertices that are mutually non-adjacent). Furthermore, the eigenvalue, diameter, girth, and clique number of their zero divisor graphs has been determined. Additionally, a conjecture on the zero divisors of T(zZp*) for integer k > 2 has been proposed. © 2025 American Institute of Physics Inc.. All rights reserved.
Mathematics Department, Faculty ofMathematics and Natural Science, Universitas Negeri Malang, Malang, Indonesia
