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The general Randić index of trees with given number of pendent vertices

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  • Cui, Qing
  • Zhong, Lingping

Abstract

The general Randić index of a graph G is defined as Rα(G)=∑uv∈E(G)(d(u)d(v))α, where d(u) denotes the degree of a vertex u in G and α is a real number. In this paper, we determine the maximum general Randić indices of trees and chemical trees with n vertices and k pendent vertices for 4≤k≤⌊n+23⌋ and α0 ≤ α < 0, where α0≈−0.5122 is the unique non-zero root of the equation 6·4α−20·9α+10·12α−16α+5·24α=0. The corresponding extremal graphs are also characterized.

Suggested Citation

  • Cui, Qing & Zhong, Lingping, 2017. "The general Randić index of trees with given number of pendent vertices," Applied Mathematics and Computation, Elsevier, vol. 302(C), pages 111-121.
    • Handle: RePEc:eee:apmaco:v:302:y:2017:i:c:p:111-121
    DOI: 10.1016/j.amc.2017.01.021
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    References listed on IDEAS

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    1. Li, Fengwei & Ye, Qingfang, 2016. "The general connectivity indices of fluoranthene-type benzenoid systems," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 897-911.
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    7. Su, Guifu & Tu, Jianhua & Das, Kinkar Ch., 2015. "Graphs with fixed number of pendent vertices and minimal Zeroth-order general Randić index," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 705-710.
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    Cited by:

    1. Ghalavand, Ali & Reza Ashrafi, Ali, 2018. "Ordering chemical graphs by Randić and sum-connectivity numbers," Applied Mathematics and Computation, Elsevier, vol. 331(C), pages 160-168.
    2. Lan, Yongxin & Li, Tao & Wang, Hua & Xia, Chengyi, 2019. "A note on extremal trees with degree conditions," Applied Mathematics and Computation, Elsevier, vol. 341(C), pages 70-79.

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