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On the metric dimension of infinite graphs

Autor
Hernando, M.; Mora, M.; Pelayo, I. M.
Tipus d'activitat
Article en revista
Revista
Electronic notes in discrete mathematics
Data de publicació
2009-11-04
Volum
35
Pàgina inicial
15
Pàgina final
20
DOI
https://doi.org/10.1016/j.endm.2009.11.004 Obrir en finestra nova
Repositori
http://hdl.handle.net/2117/8260 Obrir en finestra nova
URL
http://www.sciencedirect.com/science/journal/15710653 Obrir en finestra nova
Resum
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 a graph G is the minimum cardinality of a resolving set. In this paper we undertake the metric dimension of infinite locally finite graphs, i.e., those infinite graphs such that all its vertices have finite degree. We give some necessary conditions for an infinite graph to have finite metric dimension and characterize infinite trees with...
Citació
Hernando, M.; Mora, M.; Pelayo, I. On the metric dimension of infinite graphs. "Electronic notes in discrete mathematics", 04 Novembre 2009, vol. 35, p. 15-20.
Paraules clau
Cartesian product, graph theory, infinite graph, locally finite graph, metric dimension, resolving set
Grup de recerca
COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions
DCG - Discrete and Combinatorial Geometry