Labeled trees generating complete, compact, and discrete ultrametric spaces

2021/01/03 by Oleksiy Dovgoshey, Dovgoshey, Oleksiy, Mehmet Küçükaslan +1 · 6 citations
Mathematics · #05C05 #Advanced Topics in Algebra #Combinatorics (math.CO) #FOS: Mathematics #Fixed Point Theorems Analysis #Primary 05C63 #Secondary 54E35 #advanced mathematical theories #math.CO #msc:05C05 #msc:05C63 #msc:54E35

paper · pdf · doi:10.48550/arxiv.2101.00626

23 pages, 5 figures

openalex publication_date 2021/01/03 · arxiv created 2022/01/26 · arxiv updated 2022/01/27 · openalex created_date 2022/07/19 · openalex updated_date 2026/07/28

Abstract

We investigate the interrelations between labeled trees and ultrametric spaces generated by these trees. The labeled trees, which generate complete ultrametrics, totally bounded ultrametrics, and discrete ones, are characterized up to isomorphism. As corollary, we obtain a characterization of labeled trees generating compact ultrametrics, and discrete totally bounded ultrametrics. It is also shown that every ultrametric space generated by labeled tree contains a dense discrete subspace.

Cited by

• Longest paths in trees and isometricity of ultrametric spaces
• Forbidden Four Cycle, Star Graphs and Isometric Embeddings
• Hausdorff distance between ultrametric balls
• Labeled Trees Generating Separable and Locally Finite Ultrametrics
• The Gomory-Hu inequality and trees
• Center of distances of ultrametric spaces generated by labeled trees

Related

• Labeled Trees Generating Separable and Locally Finite Ultrametrics
• Locally finite ultrametric spaces and labeled trees
• Konig's Infinity Lemma for locally finite ultrametric spaces generated by labeled trees
• Totally bounded ultrametric spaces and locally finite trees
• Extremal properties and morphisms of finite ultrametric spaces and their representing trees