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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.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.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.rightsAttribution-NonCommercial-NoDerivs 3.0 Spain
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.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.description.peerreviewedPeer Reviewed
dc.subject.amsClassificació AMS::05 Combinatorics::05C Graph theory
dc.rights.accessRestricted access - publisher's policy
dc.description.versionPostprint (author's final draft)
upcommons.citation.authorHernando, M.; Mora, M.; Pelayo, I. M.
upcommons.citation.publicationNameDiscrete applied mathematics

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