### The Wiener Polynomial of a Graph

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.