Order-Sensitive Domination in Partially Ordered Sets and Graphs

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dc.authoridDeniz, Zakir/0000-0002-0701-0397
dc.authoridYetim, Mehmet Akif/0000-0002-3482-5137
dc.authorwosidDeniz, Zakir/AAK-6689-2021
dc.authorwosidYetim, Mehmet Akif/AAV-5238-2021
dc.contributor.authorCivan, Yusuf
dc.contributor.authorDeniz, Zakir
dc.contributor.authorYetim, Mehmet Akif
dc.date.accessioned2023-07-26T11:57:38Z
dc.date.available2023-07-26T11:57:38Z
dc.date.issued2022
dc.departmentDÜ, Fen-Edebiyat Fakültesi, Matematik Bölümüen_US
dc.description.abstractFor a (finite) partially ordered set (poset) P, we call a dominating set D in the comparability graph of P, an order-sensitive dominating set in P if either x is an element of D or else a < x < b in P for some a,b is an element of D for every element x in P which is neither maximal nor minimal, and denote by gamma(os)(P), the least size of an order-sensitive dominating set of P. For every graph G and integer k >= 2, we associate to G a graded poset P-k(G) of height k, and prove that gamma(os)(P-3(G)) = gamma(R)(G) and gamma(os)(P-4(G)) = 2 gamma(G) hold, where gamma(G) and gamma(R)(G) are the domination and Roman domination number of G respectively. Moreover, we show that the order-sensitive domination number of a poset P exactly corresponds to the biclique vertex-partition number of the associated bipartite transformation of P.en_US
dc.identifier.doi10.1007/s11083-022-09599-2
dc.identifier.issn0167-8094
dc.identifier.issn1572-9273
dc.identifier.scopus2-s2.0-85128886582en_US
dc.identifier.scopusqualityQ3en_US
dc.identifier.urihttps://doi.org/10.1007/s11083-022-09599-2
dc.identifier.urihttps://hdl.handle.net/20.500.12684/13256
dc.identifier.wosWOS:000794894800001en_US
dc.identifier.wosqualityQ4en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.institutionauthorDeniz, Zakir
dc.language.isoenen_US
dc.publisherSpringeren_US
dc.relation.ispartofOrder-A Journal on The Theory of Ordered Sets and Its Applicationsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.snmz$2023V1Guncelleme$en_US
dc.subjectDomination; Partially Ordered Set; Order-Sensitive; Comparability; Roman Domination; Biclique Vertex-Partitionen_US
dc.titleOrder-Sensitive Domination in Partially Ordered Sets and Graphsen_US
dc.typeArticleen_US

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