  A difference vertex labeling of a graph G is an assignment f of labels to the
vertices of G that induces for each edge xy the weight |f(x)-f(y)|. A
difference vertex labeling f of a graph G of size n is odd-graceful if f is an
injection from V(G) to {0,1,...,2n-1} such that the induced weights are
{1,3,...,2n-1}. We show here that any forest whose components are caterpillars
is odd-graceful. We also show that every tree of diameter up to five is
odd-graceful.
