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arXiv · 2501.01744

On the uniqueness of continuation of a partially defined metric

Evgeniy Petrov
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Abstract

The problem of continuation of a partially defined metric can be efficiently studied using graph theory. Let $G=G(V,E)$ be an undirected graph with the set of vertices $V$ and the set of edges $E$. A necessary and sufficient condition under which the weight $w\colon E\to\mathbb R^+$ on the graph $G$ has a unique continuation to a metric $d\colon V\times V\to\mathbb R^+$ is found.

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Evgeniy Petrov. 2025-01-03. On the uniqueness of continuation of a partially defined metric. https://doi.org/10.20429/tag.2022.100101

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