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Resolving dominating partitions in graphs
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.available | 2021-08-15T00:31:04Z |
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 | Open Access |
local.identifier.drac | 23580209 |
dc.description.version | Postprint (author's final draft) |
dc.relation.projectid | info:eu-repo/grantAgreement/EC/H2020/734922/EU/Combinatorics of Networks and Computation/CONNECT |
local.citation.author | Hernando, M.; Mora, M.; Pelayo, I. M. |
local.citation.publicationName | Discrete applied mathematics |
local.citation.volume | 266 |
local.citation.startingPage | 237 |
local.citation.endingPage | 251 |
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