The Wiener polynomial of a graph
Combinatorics
2007-05-23 v1
Abstract
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.
Cite
@article{arxiv.math/9801011,
title = {The Wiener polynomial of a graph},
author = {Bruce E. Sagan and Yeong-Nan Yeh and Ping Zhang},
journal= {arXiv preprint arXiv:math/9801011},
year = {2007}
}
Comments
20 pages, 2 figures, Latex, see related papers at http://www.math.msu.edu/~sagan