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Comparison between the zeroth-order Randić index and the sum-connectivity index

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  • Das, Kinkar Ch.
  • Dehmer, Matthias

Abstract

The zeroth-order Randić index and the sum-connectivity index are very popular topological indices in mathematical chemistry. These two indices are based on vertex degrees of graphs and attracted a lot of attention in recent years. Recently Li and Li (2015) studied these two indices for trees of order n. In this paper we obtain a relation between the zeroth-order Randić index and the sum-connectivity index for graphs. From this we infer an upper bound for the sum-connectivity index of graphs. Moreover, we prove that the zeroth-order Randić index is greater than the sum-connectivity index for trees. Finally, we show that R2, α(G) is greater or equal R1, α(G) (α ≥ 1) for any graph and characterize the extremal graphs.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:274:y:2016:i:c:p:585-589
    DOI: 10.1016/j.amc.2015.11.029
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    References listed on IDEAS

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    1. 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.
    2. 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. 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.

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