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On the Wiener Indices of Trees Ordering by Diameter-Growing Transformation Relative to the Pendent Edges

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  • Xiaoxin Xu
  • Yubin Gao
  • Yanbin Sang
  • Yueliang Liang

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 index 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.

Suggested Citation

  • Xiaoxin Xu & Yubin Gao & Yanbin Sang & Yueliang Liang, 2019. "On the Wiener Indices of Trees Ordering by Diameter-Growing Transformation Relative to the Pendent Edges," Mathematical Problems in Engineering, Hindawi, vol. 2019, pages 1-11, February.
    • Handle: RePEc:hin:jnlmpe:8769428
    DOI: 10.1155/2019/8769428
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