Exploring Ring Structures: Multiset Dimension Analysis in Compressed Zero-Divisor Graphs

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dc.authoridASAD, JIHAD/0000-0002-6862-1634
dc.authoridAli, Nasir/0000-0003-4116-9673
dc.authoridSiddiqui, Hafiz Muhammad Afzal/0000-0003-1794-6460
dc.authoridQureshi, Muhammad Imran/0000-0002-0681-6313
dc.contributor.authorAli, Nasir
dc.contributor.authorSiddiqui, Hafiz Muhammad Afzal
dc.contributor.authorQureshi, Muhammad Imran
dc.contributor.authorAbdallah, Suhad Ali Osman
dc.contributor.authorAlmahri, Albandary
dc.contributor.authorAsad, Jihad
dc.contributor.authorAkgul, Ali
dc.date.accessioned2024-12-24T19:33:47Z
dc.date.available2024-12-24T19:33:47Z
dc.date.issued2024
dc.departmentSiirt Üniversitesi
dc.description.abstractThis paper explores the concept of multiset dimensions (Mdim) of compressed zero-divisor graphs (CZDGs) associated with rings. The authors investigate the interplay between the ring-theoretic properties of a ring R and the associated compressed zero-divisor graph. An undirected graph consisting of a vertex set Z(RE)\{[0]}=RE\{[0],[1]}, where RE={[x] :x is an element of R} and [x]={y is an element of R : ann(x)=ann(y)} is called a compressed zero-divisor graph, denoted by Gamma ER. An edge is formed between two vertices [x] and [y] of Z(RE) if and only if [x][y]=[xy]=[0], that is, iff xy=0. For a ring R, graph G is said to be realizable as Gamma ER if G is isomorphic to Gamma ER. We classify the rings based on Mdim of their associated CZDGs and obtain the bounds for the Mdim of the compressed zero-divisor graphs. We also study the Mdim of realizable graphs of rings. Moreover, some examples are provided to support our results. Notably, we discuss the interconnection between Mdim, girth, and diameter of CZDGs, elucidating their symmetrical significance.
dc.description.sponsorshipKing Khalid University [RGP. 2/449/44]
dc.description.sponsorshipThe current work was assisted financially by the Dean of Science and Research at King Khalid University via the Large Group Project under grant number RGP. 2/449/44.
dc.identifier.doi10.3390/sym16070930
dc.identifier.issn2073-8994
dc.identifier.issue7
dc.identifier.scopus2-s2.0-85199920505
dc.identifier.scopusqualityQ1
dc.identifier.urihttps://doi.org/10.3390/sym16070930
dc.identifier.urihttps://hdl.handle.net/20.500.12604/8296
dc.identifier.volume16
dc.identifier.wosWOS:001277458500001
dc.identifier.wosqualityN/A
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherMdpi
dc.relation.ispartofSymmetry-Basel
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.subjectequivalence classes
dc.subjectmetric-dimension
dc.subjectcompressed zero-divisor graph
dc.titleExploring Ring Structures: Multiset Dimension Analysis in Compressed Zero-Divisor Graphs
dc.typeArticle

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