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On the metric dimension of infinite graphs

Autor
Cáceres, José.; Hernando, M.; Mora, M.; Pelayo, I. M.; Puertas, M. Luz
Tipus d'activitat
Article en revista
Revista
Discrete applied mathematics
Data de publicació
2012-12-07
Volum
160
Número
18
Pàgina inicial
2618
Pàgina final
2626
DOI
https://doi.org/10.1016/j.dam.2011.12.009 Obrir en finestra nova
Repositori
http://hdl.handle.net/2117/17651 Obrir en finestra nova
URL
http://www.sciencedirect.com/science/article/pii/S0166218X11004987 Obrir en finestra nova
Resum
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 me...
Citació
Cáceres, José. [et al.]. On the metric dimension of infinite graphs. "Discrete applied mathematics", 07 Desembre 2012, vol. 160, núm. 18, p. 2618-2626.
Grup de recerca
COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions
DCG - Discrete and Combinatorial Geometry

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