2009/04/30 by J. Cáceres, José Cáceres, Carmen Hernando +12
Computer Science · Engineering · Mathematics · #05C12 #05C35 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #graph theory and CDMA systems #math.CO #msc:05C12 #msc:05C35
paper · pdf · doi:10.48550/arxiv.0904.4826
17 pages, 17 figures, 3 tables, 16 references
arxiv created 2009/04/30 · openalex publication_date 2009/04/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A set of vertices S resolves 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.