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dc.contributor.authorHernando Martín, María del Carmen
dc.contributor.authorMora Giné, Mercè
dc.contributor.authorPelayo Melero, Ignacio Manuel
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.date.accessioned2019-10-30T07:02:05Z
dc.date.issued2019-01-01
dc.identifier.citationHernando, M.; Mora, M.; Pelayo, I. M. Resolving dominating partitions in graphs. "Discrete applied mathematics", 1 Gener 2019, vol. 266, p. 237-251.
dc.identifier.issn0166-218X
dc.identifier.urihttp://hdl.handle.net/2117/171094
dc.description.abstractA partition ¿ ={S1,...,Sk}of the vertex set of a connected graphGis called aresolvingpartitionofGif for every pair of verticesuandv,d(u,Sj)6=d(v,Sj), for some partSj. Thepartition dimensionßp(G) is the minimum cardinality of a resolving partition ofG. A resolvingpartition ¿ is calledresolving dominatingif for every vertexvofG,d(v,Sj) = 1, for some partSjof ¿. Thedominating partition dimension¿p(G) is the minimum cardinality of a resolvingdominating partition ofG.In this paper we show, among other results, thatßp(G)=¿p(G)=ßp(G) + 1. We alsocharacterize all connected graphs of ordern=7 satisfying any of the following conditions:¿p(G) =n,¿p(G) =n-1,¿p(G) =n-2 andßp(G) =n-2. Finally, we present some tightNordhaus-Gaddum bounds for both the partition dimensionßp(G) and the dominating partitiondimension¿p(G).
dc.format.extent15 p.
dc.language.isoeng
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 Spain
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística
dc.subject.lcshGraph theory
dc.subject.otherResolving partition
dc.subject.otherResolving dominating partition
dc.subject.otherMetric location
dc.subject.otherResolving domination
dc.subject.otherPartition dimension
dc.subject.otherDominating partition dimension
dc.titleResolving dominating partitions in graphs
dc.typeArticle
dc.subject.lemacGrafs, Teoria de
dc.contributor.groupUniversitat Politècnica de Catalunya. DCG - Discrete and Combinatorial Geometry
dc.contributor.groupUniversitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions
dc.identifier.doi10.1016/j.dam.2018.12.001
dc.description.peerreviewedPeer Reviewed
dc.subject.amsClassificació AMS::05 Combinatorics::05C Graph theory
dc.relation.publisherversionhttps://www.sciencedirect.com/science/article/pii/S0166218X18306401
dc.rights.accessRestricted access - publisher's policy
drac.iddocument23580209
dc.description.versionPostprint (author's final draft)
dc.date.lift2021-08-15
upcommons.citation.authorHernando, M.; Mora, M.; Pelayo, I. M.
upcommons.citation.publishedtrue
upcommons.citation.publicationNameDiscrete applied mathematics
upcommons.citation.volume266
upcommons.citation.startingPage237
upcommons.citation.endingPage251


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