  We investigate the interrelations between labeled trees and ultrametric
spaces generated by these trees. The labeled trees, which generate complete
ultrametrics, totally bounded ultrametrics, and discrete ones, are
characterized up to isomorphism. As corollary, we obtain a characterization of
labeled trees generating compact ultrametrics, and discrete totally bounded
ultrametrics. It is also shown that every ultrametric space generated by
labeled tree contains a dense discrete subspace.
