On the uniqueness of continuation of a partially defined metric

Authors

Evgeniy Petrov, Institute of Applied Mathematics and Mechanics of the NAS of UkraineFollow

Publication Date

January 2023

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 → R⁺ on the graph G has a unique continuation to a metric d : V x V → R⁺ is found.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.

Recommended Citation

Petrov, Evgeniy (2023) "On the uniqueness of continuation of a partially defined metric," Theory and Applications of Graphs: Vol. 10: Iss. 1, Article 1.
DOI: 10.20429/tag.2022.100101
Available at: https://digitalcommons.georgiasouthern.edu/tag/vol10/iss1/1