Isomorphism of trees and isometry of ultrametric spaces

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.