On the Wiener Indices of Trees Ordering by Diameter-Growing Transformation Relative to the Pendent Edges. (6th February 2019)

• Record Type: Journal Article
• Authors: Xu, Xiaoxin; Gao, Yubin; Sang, Yanbin; Liang, Yueliang
• Other Names: Loiseau Jean Jacques Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2019(2019)
• Publication Date: 2019-02-06
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2019/8769428
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : 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 indexW ( 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.