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The asymptotic value of the zeroth-order Randić index and sum-connectivity index for trees

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  • Li, Jing
  • Li, Yiyang

Abstract

The zeroth-order Randić index and sum–connectivity index are two indices based on the vertex degrees. They appeared in the topological formula for the total π-electron energy of conjugated molecules and attracted a lot of attention in recent years. Let Tn be the set of trees of order n. Suppose each tree in Tn is equally likely. We get that for almost every tree, the zeroth-order Randić index is among (r1 ± ε)n and the sum–connectivity index is among (r2 ± ε)n, where r1, r2 are some constants and ε is any positive real number.

Suggested Citation

  • Li, Jing & Li, Yiyang, 2015. "The asymptotic value of the zeroth-order Randić index and sum-connectivity index for trees," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 1027-1030.
    • Handle: RePEc:eee:apmaco:v:266:y:2015:i:c:p:1027-1030
    DOI: 10.1016/j.amc.2015.06.028
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    Cited by:

    1. Das, Kinkar Ch. & Dehmer, Matthias, 2016. "Comparison between the zeroth-order Randić index and the sum-connectivity index," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 585-589.
    2. Das, Kinkar Ch., 2016. "On the Graovac–Ghorbani index of graphs," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 353-360.
    3. 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.
    4. Hua, Hongbo & Das, Kinkar Ch., 2016. "On the Wiener polarity index of graphs," Applied Mathematics and Computation, Elsevier, vol. 280(C), pages 162-167.

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