Labeled trees generating complete, compact, and discrete ultrametric spaces

2021/01/03 by Dovgoshey, Oleksiy, Küçükaslan, Mehmet · 3 citations
#05C05 #Combinatorics (math.CO) #FOS: Mathematics #Primary 05C63 #Secondary 54E35

paper · doi:10.48550/arxiv.2101.00626

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

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• Extremal properties and morphisms of finite ultrametric spaces and their representing trees