  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.
