Ultrametric spaces generated by labeled star graphs

2025/02/03 by Oleksiy Dovgoshey, Olga Rovenska, Dovgoshey, Oleksiy +1 · 1 voice · 6 citations
Computer Science · Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Fixed Point Theorems Analysis #General Topology (math.GN) #Graph Labeling and Dimension Problems #Primary 54E35 #Secondary 54E4 #math.GN

paper · pdf · doi:10.48550/arxiv.2502.01260

openalex publication_date 2025/02/03 · arxiv published 2025/02/03 · arxiv updated 2025/02/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For arbitrary star graph S with a non-degenerate vertex labeling l\colon V(S) → ℝ⁺ we denote by d_l the corresponding ultrametric on the vertex set V(S) of S. We characterize the class \bf US of all ultrametric spaces (V(S), d_l) up to isometry. We also find the necessary and sufficient conditions under which the group of all self-isometries of ultrametric space (V(S), d_l) coincides with the group of all self-isomorphisms of the labeled star graph S(l).

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

Discussions

• Oleksiy Dovgoshey, Olga Rovenska: Ultrametric spaces generated by labeled star graphs https://arxiv.org/abs/2502.01260 https://arxiv.org/pdf/2502.01260 https://arxiv.org/html/2502.01260 [bsky, 0 points, 1 comments]

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