  The Wiener index is a graphical invariant that has found extensive
application in chemistry. We define a generating function, which we call the
Wiener polynomial, whose derivative is a q-analog of the Wiener index. We study
some of the elementary properties of this polynomial and compute it for some
common graphs. We then find a formula for the Wiener polynomial of a dendrimer,
a certain highly regular tree of interest to chemists, and show that it is
unimodal. Finally, we point out a connection with the Poincare polynomial of a
finite Coxeter group.
