On the uniqueness of continuation of a partially defined metric
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866913634338209792 |
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| author | Petrov, Evgeniy |
| author_facet | Petrov, Evgeniy |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_01744 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the uniqueness of continuation of a partially defined metric Petrov, Evgeniy General Topology 05C12, 54E35 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. |
| title | On the uniqueness of continuation of a partially defined metric |
| topic | General Topology 05C12, 54E35 |
| url | https://arxiv.org/abs/2501.01744 |