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The Wiener polynomial of a graph
Author(s) -
Sagan Bruce E.,
Yeh YeongNan,
Zhang Ping
Publication year - 1996
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/(sici)1097-461x(1996)60:5<959::aid-qua2>3.0.co;2-w
Subject(s) - wiener index , polynomial , mathematics , combinatorics , invariant (physics) , graph , discrete mathematics , pure mathematics , mathematical analysis , mathematical physics
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 Poincaré polynomial of a finite Coxeter group. © 1996 John Wiley & Sons, Inc.