On the uniqueness of continuation of a partially defined metric

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 $w:E\to {\mathbb{R}}^{+}$ on the graph $G$ has a unique continuation to a metric $d:V\times V\to {\mathbb{R}}^{+}$ is found.

7 pages, This is the submitted version. The published version is available at https://doi.org/10.20429/tag.2022.100101

References in corpus (1)

• On the uniqueness of continuation of a partially defined metric

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