Extremal Trees of Terminal Wiener Index

  • Dan-fang Chen
  • Fu-yi Wei
  • Hong-ying Zhu
  • Yang Wu
  • Shan-zhang Nong
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 367)

Abstract

The generalized Terminal Wiener Index is the sum of distances between each pair of vertices of degree k. In this paper, we proved the conjecture of reference [1]: when \({\text {k}}\ge 4\), the generalized terminal Wiener index of trees reaches its maximum value at \({\text {T}}_{{{\text {n}},{\text {k}},{\text {p}}}}\) caterpillars. We also determined the corresponding p value of the extremal graph.

Keywords

Wiener index Generalized terminal wiener index Maximum  Extremal graph Caterpillar 

Notes

Acknowledgments

Support of the training and plan projects of college student’s innovation and pioneering in Guangzhou Province (No. 1056413046) is gratefully acknowledged. We are also grateful to the referees for their valuable comments and corrections, which lead to an improvement of the original manuscript.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Dan-fang Chen
    • 1
  • Fu-yi Wei
    • 1
  • Hong-ying Zhu
    • 1
  • Yang Wu
    • 1
  • Shan-zhang Nong
    • 1
  1. 1.College of ScienceSouth China Agricultural UniversityGuangzhouChina

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