dc.contributor.author Hernando Martín, María del Carmen dc.contributor.author Mora Giné, Mercè dc.contributor.author Pelayo Melero, Ignacio Manuel dc.contributor.other Universitat Politècnica de Catalunya. Departament de Matemàtiques dc.date.accessioned 2019-10-30T07:02:05Z dc.date.issued 2019-01-01 dc.identifier.citation Hernando, M.; Mora, M.; Pelayo, I. M. Resolving dominating partitions in graphs. "Discrete applied mathematics", 1 Gener 2019, vol. 266, p. 237-251. dc.identifier.issn 0166-218X dc.identifier.uri http://hdl.handle.net/2117/171094 dc.description.abstract A 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.extent 15 p. dc.language.iso eng dc.rights Attribution-NonCommercial-NoDerivs 3.0 Spain dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/3.0/es/ dc.subject Àrees temàtiques de la UPC::Matemàtiques i estadística dc.subject.lcsh Graph theory dc.subject.other Resolving partition dc.subject.other Resolving dominating partition dc.subject.other Metric location dc.subject.other Resolving domination dc.subject.other Partition dimension dc.subject.other Dominating partition dimension dc.title Resolving dominating partitions in graphs dc.type Article dc.subject.lemac Grafs, Teoria de dc.contributor.group Universitat Politècnica de Catalunya. DCG - Discrete and Combinatorial Geometry dc.contributor.group Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions dc.identifier.doi 10.1016/j.dam.2018.12.001 dc.description.peerreviewed Peer Reviewed dc.subject.ams Classificació AMS::05 Combinatorics::05C Graph theory dc.relation.publisherversion https://www.sciencedirect.com/science/article/pii/S0166218X18306401 dc.rights.access Restricted access - publisher's policy drac.iddocument 23580209 dc.description.version Postprint (author's final draft) dc.date.lift 2021-08-15 upcommons.citation.author Hernando, M.; Mora, M.; Pelayo, I. M. upcommons.citation.published true upcommons.citation.publicationName Discrete applied mathematics upcommons.citation.volume 266 upcommons.citation.startingPage 237 upcommons.citation.endingPage 251
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