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dc.contributor.authorNaji, Ahmed Mohammeden_US
dc.contributor.authorNandappa D., Soneren_US
dc.date.accessioned2020-10-12T08:04:00Z
dc.date.available2020-10-12T08:04:00Z
dc.date.issued2017
dc.identifier.citationNaji, A. M. & Nandappa D., S. (2017). Partitioning a graph into monopoly sets. TWMS Journal Of Applied And Engineering Mathematics, 7(1), 154-164.en_US
dc.identifier.issn2146-1147en_US
dc.identifier.issn2587-1013en_US
dc.identifier.urihttp://belgelik.isikun.edu.tr/xmlui/handle/iubelgelik/2619
dc.identifier.urihttp://jaem.isikun.edu.tr/web/index.php/archive/93-vol7no1/287
dc.description.abstractIn a graph G = (V, E), a set M ? V (G) is said to be a monopoly set of G if every vertex v ? V ? M has, at least, d(v)/2 neighbors in M. The monopoly size of G, denoted by mo(G), is the minimum cardinality of a monopoly set. In this paper, we study the problem of partitioning V (G) into monopoly sets. An M-partition of a graph G is the partition of V (G) into k disjoint monopoly sets. The monatic number of G, denoted by µ(G), is the maximum number of sets in M-partition of G. It is shown that 2 ? µ(G) ? 3 for every graph G without isolated vertices. The properties of each monopoly partite set of G are presented. Moreover, the properties of all graphs G having µ(G) = 3, are presented. It is shown that every graph G having µ(G) = 3 is Eulerian and have ?(G) ? 3. Finally, it is shown that for every integer k /? {1, 2, 4}, there exists a graph G of order n = k having µ(G) = 3.en_US
dc.language.isoenen_US
dc.publisherIşık University Pressen_US
dc.relation.ispartofTWMS Journal Of Applied And Engineering Mathematicsen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 United States*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/us/*
dc.subjectVertex degreesen_US
dc.subjectDistance in graphsen_US
dc.subjectGraph polynomialsen_US
dc.subjectDynamic monopoliesen_US
dc.subjectCoalitionsen_US
dc.titlePartitioning a graph into monopoly setsen_US
dc.typeArticleen_US
dc.description.versionPublisher's Versionen_US
dc.identifier.volume7
dc.identifier.issue1
dc.identifier.startpage154
dc.identifier.endpage164
dc.peerreviewedYesen_US
dc.publicationstatusPublisheden_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Başka Kurum Yazarıen_US


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