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Título: | Resolving dominating partitions in graphs |
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Autor/a: | Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel |
Otros autores: | Universitat Politècnica de Catalunya. Departament de Matemàtiques; Universitat Politècnica de Catalunya. DCG - Discrete and Combinatorial Geometry; Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions |
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). |
Abstract: | Peer Reviewed |
Materia(s): | -Àrees temàtiques de la UPC::Matemàtiques i estadística -Graph theory -Resolving partition -Resolving dominating partition -Metric location -Resolving domination -Partition dimension -Dominating partition dimension -Grafs, Teoria de -Classificació AMS::05 Combinatorics::05C Graph theory |
Derechos: | Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
Tipo de documento: | Artículo - Versión presentada Artículo |
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