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Ordering chemical graphs by Randić and sum-connectivity numbers

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  • Ghalavand, Ali
  • Reza Ashrafi, Ali

Abstract

Let G be a graph with edge set E(G). The Randić and sum-connectivity indices of G are defined as R(G)=∑uv∈E(G)1degG(u)degG(v) and SCI(G)=∑uv∈E(G)1degG(u)+degG(v), respectively, where degG(u) denotes the vertex degree of u in G. In this paper, the extremal Randić and sum-connectivity index among all n-vertex chemical trees, n ≥ 13, connected chemical unicyclic graphs, n ≥ 7, connected chemical bicyclic graphs, n ≥ 6 and connected chemical tricyclic graphs, n ≥ 8, were presented.

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  • 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.
    • Handle: RePEc:eee:apmaco:v:331:y:2018:i:c:p:160-168
    DOI: 10.1016/j.amc.2018.02.049
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    References listed on IDEAS

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    1. Ghalavand, A. & Ashrafi, A.R., 2017. "Extremal graphs with respect to variable sum exdeg index via majorization," Applied Mathematics and Computation, Elsevier, vol. 303(C), pages 19-23.
    2. 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.
    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. Shi, Yongtang, 2015. "Note on two generalizations of the Randić index," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 1019-1025.
    5. Ashrafi, Ali Reza & Ghalavand, Ali, 2017. "Ordering chemical trees by Wiener polarity index," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 301-312.
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    Cited by:

    1. Yang, Yu & Fan, Ai-wan & Wang, Hua & Lv, Hailian & Zhang, Xiao-Dong, 2019. "Multi-distance granularity structural α-subtree index of generalized Bethe trees," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 107-120.

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