On Certain Bounds for Multiset Dimensions of Zero-Divisor Graphs Associated with Rings

2024/05/10 by Nasir Ali, Ali, Nasir, Hafiz Muhammad Afzal Siddiqui +3
Computer Science · Mathematics · #Advanced Topics in Algebra #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2405.06180

openalex publication_date 2024/05/10 · openalex created_date 2024/05/14 · openalex updated_date 2026/07/28

Abstract

This article investigates multiset dimensions in zero divisor graphs (ZD-graphs) associated with rings. Through rigorous analysis, we establish general bounds for the multiset dimension (Mdim) in ZD-graphs, exploring various commutative rings including the ring Z_n of integers modulo n, Gaussian integers and quotient polynomial rings. Additionally, we examine the behavior of Mdim under algebraic operations and discuss bounds in terms of diameter and maximum degree. This study enhances our understanding of algebraic structures and their graphical representations.

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