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

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arxiv 2405.06180 v2 pith:NZHPVFE5 submitted 2024-05-10 math.CO

Nasir Ali , Hafiz Muhammad Afzal Siddiqui , Muhammad Imran Qureshi This is my paper · ORCID
classification math.CO
keywords ringsboundsmultisetalgebraicassociateddimensionsgraphsintegers
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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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  1. Multiset resolvability parameters in graphs: A survey with new results and open problems

    math.CO 2026-07 accept novelty 5.0 of 10

    Multiset resolvability parameters are surveyed; sharp outer-multiset lower bounds for diameter-two and join graphs are proved, and block graphs with local multiset dimension two are characterized.

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