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Extremal trees for the Randić index with given domination number

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  • Bermudo, Sergio
  • Nápoles, Juan E.
  • Rada, Juan

Abstract

The Randić index is the topological index most widely used in applications for chemistry and pharmacology. It is defined for a graph G with vertex set V(G) and edge set E(G) asR(G)=∑uv∈E(G)1deg(u)deg(v),where deg(u) and deg(v) denote the degrees of the vertices u, v ∈ V(G). In this paper we find upper and lower bounds of the Randić index of trees in terms of the order and the domination number. The extremal trees are characterized.

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  • Bermudo, Sergio & Nápoles, Juan E. & Rada, Juan, 2020. "Extremal trees for the Randić index with given domination number," Applied Mathematics and Computation, Elsevier, vol. 375(C).
    • Handle: RePEc:eee:apmaco:v:375:y:2020:i:c:s0096300320300916
    DOI: 10.1016/j.amc.2020.125122
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    References listed on IDEAS

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    1. Shuchao Li & Huihui Zhang, 2016. "Some extremal properties of the multiplicatively weighted Harary index of a graph," Journal of Combinatorial Optimization, Springer, vol. 31(3), pages 961-978, April.
    2. Borovićanin, Bojana & Furtula, Boris, 2016. "On extremal Zagreb indices of trees with given domination number," Applied Mathematics and Computation, Elsevier, vol. 279(C), pages 208-218.
    3. Shuchao Li & Xian Meng, 2015. "Four edge-grafting theorems on the reciprocal degree distance of graphs and their applications," Journal of Combinatorial Optimization, Springer, vol. 30(3), pages 468-488, October.
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    Cited by:

    1. Ayu Ameliatul Shahilah Ahmad Jamri & Fateme Movahedi & Roslan Hasni & Rudrusamy Gobithaasan & Mohammad Hadi Akhbari, 2022. "Minimum Randić Index of Trees with Fixed Total Domination Number," Mathematics, MDPI, vol. 10(20), pages 1-13, October.

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    Keywords

    Randić index; Domination number;

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