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Extremal graph theory for metric dimension and diameter
dc.contributor.author | Hernando Martín, María del Carmen |
dc.contributor.author | Mora Giné, Mercè |
dc.contributor.author | Seara Ojea, Carlos |
dc.contributor.author | Wood, David |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II |
dc.date.accessioned | 2010-07-20T09:42:46Z |
dc.date.available | 2010-07-20T09:42:46Z |
dc.date.created | 2010-02-22 |
dc.date.issued | 2010-02-22 |
dc.identifier.citation | Hernando, M. [et al.]. Extremal graph theory for metric dimension and diameter. "Electronic journal of combinatorics", 22 Febrer 2010, vol. 17, núm. R30, p. 1-28. |
dc.identifier.issn | 1077-8926 |
dc.identifier.uri | http://hdl.handle.net/2117/8261 |
dc.description.abstract | A set of vertices S resolves a connected graph G if every vertex is uniquely determined by its vector of distances to the vertices in S. The metric dimension of G is the minimum cardinality of a resolving set of G. Let G ,D be the set of graphs with metric dimension and diameter D. It is well-known that the minimum order of a graph in G ,D is exactly + D. The first contribution of this paper is to characterise the graphs in G ,D with order + D for all values of and D. Such a characterisation was previously only known for D 6 2 or 6 1. The second contribution is to determine the maximum order of a graph in G ,D for all values of D and . Only a weak upper bound was previously known. |
dc.format.extent | 28 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 | order |
dc.subject.other | graph |
dc.subject.other | distance |
dc.subject.other | resolving set |
dc.subject.other | metric dimension |
dc.subject.other | metric basis |
dc.subject.other | diameter |
dc.title | Extremal graph theory for metric dimension and diameter |
dc.type | Article |
dc.subject.lemac | Grafs, Teoria de |
dc.contributor.group | Universitat Politècnica de Catalunya. DCCG - Grup de recerca en geometria computacional, combinatoria i discreta |
dc.relation.publisherversion | http://www.combinatorics.org/Volume_17/PDF/v17i1r30.pdf |
dc.rights.access | Open Access |
local.identifier.drac | 2581454 |
dc.description.version | Postprint (published version) |
local.citation.author | Hernando, M.; Mora, M.; Seara, C.; Wood, D. |
local.citation.publicationName | Electronic journal of combinatorics |
local.citation.volume | 17 |
local.citation.number | R30 |
local.citation.startingPage | 1 |
local.citation.endingPage | 28 |
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