Open AccessOn the Wiener Indices of Trees Ordering by Diameter-Growing Transformation Relative to the Pendent Edges
Author(s) -
Xiaohui Xu,
Yubin Gao,
Yanbin Sang,
Yueliang Liang
Publication year - 2019
Publication title -
mathematical problems in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.262
H-Index - 62
eISSN - 1026-7077
pISSN - 1024-123X
DOI - 10.1155/2019/8769428
Subject(s) - wiener index , transformation (genetics) , mathematics , graph , tree (set theory) , combinatorics , index (typography) , computer science , chemistry , biochemistry , world wide web , gene
The Wiener index of a graph is defined as the sum of distances between all unordered pairs of its vertices. We found that finite steps of diameter-growing transformation relative to vertices can not always enable the Wiener index of a tree to increase sharply. In this paper, we provide a graph transformation named diameter-growing transformation relative to pendent edges, which increases Wiener index W ( T ) of a tree sharply after finite steps. Then, twenty-two trees are ordered by their Wiener indices, and these trees are proved to be the first twenty-two trees with the first up to sixteenth smallest Wiener indices.