2020/03/18 by Samuel G. Corregidor, Corregidor, Samuel G., Álvaro Martínez-Pérez +1
Computer Science · Decision Sciences · #51E99 #51F99 #54E35 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Fuzzy and Soft Set Theory #General Topology (math.GN) #Graph Labeling and Dimension Problems
paper · pdf · doi:10.48550/arxiv.2003.10239
openalex publication_date 2020/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a metric space (X,d), a set S⊆ X is called a k-metric generator for X if any pair of different points of X is distinguished by at least k elements of S. A k-metric basis is a k-metric generator of the minimum cardinality in X. We prove that ultrametric spaces do not have finite k-metric bases for k>2. We also characterize when the metric and 2-metric bases of an ultrametric space are finite and, when they are finite, we characterize them. Finally, we prove that an ultrametric space can be easily recovered knowing only the metric basis and the coordinates of the points in it.