On the uniqueness of continuation of a partially defined metric

Evgeniy Petrov, Institute of Applied Mathematics and Mechanics of the NAS of Ukraine
2022 Theory and Applications of Graphs  
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 × V → R + is found.
doi:10.20429/tag.2022.100101 fatcat:eckbkfb3b5df5awd6ac67unlqi