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
On Wiener-type polynomials of thorn graphs
✍ Scribed by Bo Zhou; Damir Vukičević
- Publisher
- John Wiley and Sons
- Year
- 2009
- Tongue
- English
- Weight
- 154 KB
- Volume
- 23
- Category
- Article
- ISSN
- 0886-9383
- DOI
- 10.1002/cem.1258
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✦ Synopsis
Abstract
We derive the expressions of the ordinary, the vertex‐weighted and the doubly vertex‐weighted Wiener polynomials of a type of thorn graph, for which the number of pendant edges attached to any vertex of the underlying parent graph is a linear function of its degree. We also define variable vertex‐weighted Wiener polynomials and calculate them for the same type of thorn graphs. Copyright © 2009 John Wiley & Sons, Ltd.
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