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The Wiener polynomial of a graph

Bruce E. Sagan·Yeong-Nan Yeh·Ping Zhang
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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.

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BibTeXRIS

Bruce E. Sagan, Yeong-Nan Yeh, Ping Zhang. 1998-01-02. The Wiener polynomial of a graph. https://arxiv.org/abs/math/9801011

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