On the metric dimension of infinite graphs

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To access the full text documents, please follow this link: http://hdl.handle.net/2117/17651

dc.contributor	Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I
dc.contributor	Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II
dc.contributor	Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III
dc.contributor	Universitat Politècnica de Catalunya. DCCG - Grup de recerca en geometria computacional, combinatoria i discreta
dc.contributor	Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions
dc.contributor.author	Cáceres, José
dc.contributor.author	Hernando Martín, María del Carmen
dc.contributor.author	Mora Giné, Mercè
dc.contributor.author	Pelayo Melero, Ignacio Manuel
dc.contributor.author	Puertas, Maria Luz
dc.date	2012-12-07
dc.identifier.citation	Cáceres, José. [et al.]. On the metric dimension of infinite graphs. "Discrete applied mathematics", 07 Desembre 2012, vol. 160, núm. 18, p. 2618-2626.
dc.identifier.citation	0166-218X
dc.identifier.citation	10.1016/j.dam.2011.12.009
dc.identifier.uri	http://hdl.handle.net/2117/17651
dc.language.iso	eng
dc.relation	http://www.sciencedirect.com/science/article/pii/S0166218X11004987
dc.rights	Attribution-NonCommercial-NoDerivs 3.0 Spain
dc.rights	info:eu-repo/semantics/openAccess
dc.rights	http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subject	Àrees temàtiques de la UPC::Matemàtiques i estadística
dc.subject	Grafs, Teoria de
dc.title	On the metric dimension of infinite graphs
dc.type	info:eu-repo/semantics/publishedVersion
dc.type	info:eu-repo/semantics/article
dc.description.abstract	Infinite graph; Locally finite graph; Resolving set; Metric dimension; Cartesian product
dc.description.abstract	A set of vertices Sresolves a graph G if every vertex is uniquely determined by its vector of distances to the vertices in S. The metric dimension of a graph G is the minimum cardinality of a resolving set. In this paper we study the metric dimension of infinite graphs such that all its vertices have finite degree. We give necessary conditions for those graphs to have finite metric dimension and characterize infinite trees with finite metric dimension. We also establish some results about the metric dimension of the cartesian product of finite and infinite graphs, and give the metric dimension of the cartesian product of several families of graphs.
dc.description.abstract	Peer Reviewed

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