Domination and independence numbers of exact zero-divisor graph of the ring $\mathbb{Z}_n$

Abstract

This study examines the structural properties of exact zero-divisor graph associated with commutative rings possessing a non-zero identity, emphasizing rings that are not integral domains. By focusing on key graph-theoretic parameters, such as domination and independence numbers, we provide a detailed analysis of their behavior in specific rings, including \( \mathbb{Z}_{p^2} \), \( \mathbb{Z}_{p^k} \), and \( \mathbb{Z}_{pq} \). These findings reveal significant relationships between these parameters and the fundamental algebraic properties of rings, enhancing the comprehension of the interaction between graph theory and ring theory.