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The Wiener polynomial of a graph | | Bruce E. Sagan
; Yeong-Nan Yeh
; Ping Zhang
; | | Date: |
2 Dec 1997 | | Journal: | Internat. J. of Quantum Chem. 60 (1996), 959-969 | | Subject: | Combinatorics MSC-class: 05C12 (Primary) 05A15, 05A20, 05C05 (Secondary) | math.CO | | Affiliation: | Michigan State), Yeong-Nan Yeh (Academia Sinica), Ping Zhang (Western Michigan | | 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. | | Source: | arXiv, math.CO/9801011 | | Services: | Forum | Review | PDF | Favorites | |
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