Subdominant pseudoultrametric on graphs
Metric Geometry
2011-11-01 v1
Abstract
Let (G,w) be a weighted graph. The necessary and sufficient conditions under which a weight w : E(G)-->R^+ can be extended to a pseudoultrametric on V(G) are found. A criterion of the uniqueness of this extension is also obtained. It is proved that G is complete k-partite with k >= 2 if and only if, for every pseudoultrametrizable weight w, there exists the smallest pseudoultrametric agreed with w. We characterize the structure of graphs for which the subdominant pseudoultrametric is an ultrametric for every strictly positive pseudoultrametrizable weight.
Cite
@article{arxiv.1110.6802,
title = {Subdominant pseudoultrametric on graphs},
author = {O. Dovgoshey and E. Petrov},
journal= {arXiv preprint arXiv:1110.6802},
year = {2011}
}
Comments
22 pages, 3 figures