1998/01/02 by Bruce E. Sagan, Yeong-Nan Yeh, Ping Zhang
Mathematics · #math.CO #msc:05C12 #msc:05A15 #msc:05A20 #msc:05C05
published as Internat. J. of Quantum Chem. 60 (1996), 959-969 · 20 pages, 2 figures, Latex, see related papers at http://www.math.msu.edu/~sagan
arxiv created 1998/01/02 · arxiv updated 2009/11/30
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.