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Trees with the minimum Wiener number
Author(s) -
Liu ShuChung,
Tong LiDa,
Yeh YeongNan
Publication year - 2000
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(2000)78:5<331::aid-qua4>3.0.co;2-v
Subject(s) - wiener index , combinatorics , vertex (graph theory) , mathematics , graph , invariant (physics) , connectivity , mathematical physics
The Wiener number () of a connected graph is the sum of distances for all pairs of vertices. As a graphical invariant, it has been found extensive application in chemistry. Considering the family of trees with n vertices and a fixed maximum vertex degree, we derive some methods that can strictly reduce by shifting leaves. And then, by a process, we prove that the dendrimer on n vertices is the unique graph reaching the minimum Wiener number. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 78: 331–340, 2000