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Trees with the minimum Wiener number

✍ Scribed by Shu-Chung Liu; Li-Da Tong; Yeong-Nan Yeh

Publisher
John Wiley and Sons
Year
2000
Tongue
English
Weight
283 KB
Volume
78
Category
Article
ISSN
0020-7608

No coin nor oath required. For personal study only.

✦ Synopsis

The Wiener number (W) 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 W 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.

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