THE WIENER POLYNOMIAL OF A GRAPH

The Wiener index is a graphical invariant that has found extensive app lication in chemistry. We define a generating function, which we call the Wiener polynomial, whose derivative is a q-analog of the Wiener in dex. We study some of the elementary properties of this polynomial and compute it for some common graphs. We then find a formula for the Wie ner polynomial of a dendrimer, a certain highly regular tree of intere st to chemists, and show that it is unimodal. Finally, we point out a connection with the Poincare polynomial of a finite Coxeter group. (C) 1996 John Wiley & Sons, Inc.