Isomorphism of trees and isometry of ultrametric spaces
Oleksiy Dovgoshey

TL;DR
This paper explores the relationship between tree isomorphism and ultrametric space isometry, generalizing known results for phylogenetic and monotone trees to broader classes of tree-based metric spaces.
Contribution
It establishes conditions under which tree isomorphism corresponds to ultrametric space isometry, extending previous findings to new classes of trees.
Findings
Isometry of metric spaces corresponds to tree isomorphism under certain conditions
Generalizes known results for phylogenetic and Gurvich-Vyalyi monotone trees
Provides new criteria for tree and ultrametric space equivalence
Abstract
We study the conditions under which the isometry of spaces with metrics generated by weights given on the edges of finite trees is equivalent to the isomorphism of these trees. Similar questions are studied for ultrametric spaces generated by labelings given on the vertices of trees. The obtained results generalized some facts previously known for phylogenetic trees and for Gurvich-Vyalyi monotone trees.
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Taxonomy
Topicsadvanced mathematical theories · Topological and Geometric Data Analysis · Advanced Topology and Set Theory
