  Let F(X) be the set of finite nonempty subsets of a set X. We have found the
necessary and sufficient conditions under which for a given function f:F(X)-->R
there is an ultrametric on X such that f(A)=diam A for every A\in F(X). For
finite nondegenerate ultrametric spaces (X,d) it is shown that X together with
the subset of diametrical pairs of points of X forms a complete k-partite
graph, k>= 2, and, conversely, every finite complete k-partite graph with k>=2
can be obtained by this way. We use this result to characterize the finite
ultrametric spaces (X,d) having the minimal card{(x,y):d(x,y)=diam X, x,y \in
X} for given card X.
