2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/76455The 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.20 pages, 2 figures, Latex, see related papers at http://www.math.msu.edu/~saganCombinatorics05C12 (Primary) 05A15, 05A20, 05C05 (Secondary)text