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Minimum Randić Index of Trees with Fixed Total Domination Number

Author

Listed:
  • Ayu Ameliatul Shahilah Ahmad Jamri

    (Special Interest Group on Modelling and Data Analytics (SIGMDA), Faculty of Ocean Engineering Technology and Informatics, Universiti Malaysia Terengganu, Kuala Nerus 21030, Terengganu, Malaysia)

  • Fateme Movahedi

    (Department of Mathematics, Faculty of Sciences, Golestan University, Gorgan 15759-49138, Iran)

  • Roslan Hasni

    (Special Interest Group on Modelling and Data Analytics (SIGMDA), Faculty of Ocean Engineering Technology and Informatics, Universiti Malaysia Terengganu, Kuala Nerus 21030, Terengganu, Malaysia)

  • Rudrusamy Gobithaasan

    (Special Interest Group on Modelling and Data Analytics (SIGMDA), Faculty of Ocean Engineering Technology and Informatics, Universiti Malaysia Terengganu, Kuala Nerus 21030, Terengganu, Malaysia)

  • Mohammad Hadi Akhbari

    (Department of Mathematics, Estahban Branch, Islamic Azad University, Estahban 74518-64756, Iran)

Abstract

The Randić index is among the most famous degree-based topological indices in chemical graph theory. It was introduced due to its application in modeling the properties of certain molecular structures and has been extensively studied. In this paper, we study the lower bound of the Randić index of trees in terms of the order and the total domination number. Finally, trees with the minimal Randić index are characterized.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:20:p:3729-:d:938815
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    References listed on IDEAS

    as
    1. 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).
    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. Sun, Xiaoling & Du, Jianwei, 2022. "On Sombor index of trees with fixed domination number," Applied Mathematics and Computation, Elsevier, vol. 421(C).
    4. Wang, Shaohui & Wang, Chunxiang & Liu, Jia-Bao, 2018. "On extremal multiplicative Zagreb indices of trees with given domination number," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 338-350.
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