The Wiener polynomial of a graph

Details The Wiener polynomial of a graph The Wiener polynomial of a graph

1998-01-02

arxiv.org/abs/math/9801011v1

Internat. J. of Quantum Chem. 60 (1996), 959-969

Mathematics

Combinatorics

20 pages, 2 figures, Latex, see related papers at http://www.math.msu.edu/~sagan

Scientific paper

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.

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