A graph-theoretic approach to ring analysis: Dominant metric dimensions in zero-divisor graphs

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dc.authoridAli, Nasir/0000-0003-4116-9673
dc.contributor.authorAli, Nasir
dc.contributor.authorSiddiqui, Hafiz Muhammad Afzal
dc.contributor.authorRiaz, Muhammad Bilal
dc.contributor.authorQureshi, Muhammad Imran
dc.contributor.authorAkgul, Ali
dc.date.accessioned2024-12-24T19:27:13Z
dc.date.available2024-12-24T19:27:13Z
dc.date.issued2024
dc.departmentSiirt Üniversitesi
dc.description.abstractThis article investigates the concept of dominant metric dimensions in zero divisor graphs (ZDgraphs) associated with rings. Consider a finite commutative ring with unity, denoted as R, where nonzero elements x and y are identified as zero divisors if their product results in zero (x . y = 0). The set of zero divisors in ring R is referred to as L(R). To analyze various algebraic properties of R, a graph known as the zero-divisor graph is constructed using L(R). This manuscript establishes specific general bounds for the dominant metric dimension (Ddim) concerning the ZD-graph of R. To achieve this objective, we examine the zero divisor graphs for specific rings, such as the ring of Gaussian integers modulo m, denoted as Zm[i], the ring of integers modulo n, denoted as Zn, and some quotient polynomial rings. Our research unveils new insights into the structural similarities and differences among commutative rings sharing identical metric dimensions and dominant metric dimensions. Additionally, we present a general result outlining bounds for the dominant metric dimension expressed in terms of the maximum degree, girth, clique number, and diameter of the associated ZD-graphs. Through this exploration, we aim to provide a comprehensive framework for analyzing commutative rings and their associated zero divisor graphs, thereby advancing both theoretical knowledge and practical applications in diverse domains.
dc.description.sponsorshipEuropean Union [CZ.10.03.01/00/22_003/0000048]
dc.description.sponsorshipThis article has been produced with the financial support of the European Union under the REFRESH - Research Excellence For Region Sustainability and High-tech Industries project number CZ.10.03.01/00/22_003/0000048 via the Operational Programme Just Transition.
dc.identifier.doi10.1016/j.heliyon.2024.e30989
dc.identifier.issn2405-8440
dc.identifier.issue10
dc.identifier.pmid38813199
dc.identifier.scopus2-s2.0-85193532089
dc.identifier.scopusqualityQ1
dc.identifier.urihttps://doi.org/10.1016/j.heliyon.2024.e30989
dc.identifier.urihttps://hdl.handle.net/20.500.12604/6530
dc.identifier.volume10
dc.identifier.wosWOS:001298423700001
dc.identifier.wosqualityN/A
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.indekslendigikaynakPubMed
dc.language.isoen
dc.publisherCell Press
dc.relation.ispartofHeliyon
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_20241222
dc.subjectAlgebraic structures
dc.subjectZero divisor graphs
dc.subjectMultiset dimensions
dc.subjectMetric dimension
dc.titleA graph-theoretic approach to ring analysis: Dominant metric dimensions in zero-divisor graphs
dc.typeArticle

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