On Certain Bounds for Multiset Dimensions of Zero-Divisor Graphs Associated with Rings
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916296208154624 |
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| author | Ali, Nasir Siddiqui, Hafiz Muhammad Afzal Qureshi, Muhammad Imran |
| author_facet | Ali, Nasir Siddiqui, Hafiz Muhammad Afzal Qureshi, Muhammad Imran |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_06180 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Certain Bounds for Multiset Dimensions of Zero-Divisor Graphs Associated with Rings Ali, Nasir Siddiqui, Hafiz Muhammad Afzal Qureshi, Muhammad Imran Combinatorics 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. |
| title | On Certain Bounds for Multiset Dimensions of Zero-Divisor Graphs Associated with Rings |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2405.06180 |