Compact ultrametric spaces generated by labeled star graphs

2025/04/03 by Oleksiy Dovgoshey, Dovgoshey, Oleksiy, Omer Cantor +3 · 1 voice · 5 citations
Computer Science · Decision Sciences · Mathematics · #FOS: Mathematics #Fixed Point Theorems Analysis #Fuzzy and Soft Set Theory #General Topology (math.GN) #Graph Labeling and Dimension Problems #Primary 54E35 #Secondary 54E4 #math.GN

paper · pdf · doi:10.48550/arxiv.2504.02425

openalex publication_date 2025/04/03 · arxiv published 2025/04/03 · arxiv updated 2025/04/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let US be the class of all ultrametric spaces generated by labeled star graphs. We prove that compact US-spaces are the completions of totally bounded ultrametric spaces generated by decreasingly labeled rays. We characterize the ultrametric spaces which are weakly similar to finite US-spaces and describe these spaces by certain four-point conditions.

Cited by

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

Discussions

• Oleksiy Dovgoshey, Omer Cantor, Olga Rovenska: Compact ultrametric spaces generated by labeled star graphs https://arxiv.org/abs/2504.02425 https://arxiv.org/pdf/2504.02425 https://arxiv.org/html/2504 [bsky, 0 points, 1 comments]

Related

• Ultrametric spaces generated by labeled star graphs
• Forbidden Four Cycle, Star Graphs and Isometric Embeddings
• Labeled trees generating complete, compact, and discrete ultrametric spaces
• Labeled Trees Generating Separable and Locally Finite Ultrametrics
• Locally finite ultrametric spaces and labeled trees