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On extremal multiplicative Zagreb indices of trees with given domination number

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  • Wang, Shaohui
  • Wang, Chunxiang
  • Liu, Jia-Bao

Abstract

For a (molecular) graph, the first multiplicative Zagreb index Π1 is equal to the product of squares of the vertex degrees, and the second multiplicative Zagreb index Π2 is equal to the product of the products of degrees of pairs of adjacent vertices. In this paper, we explore the multiplicative Zagreb indices in terms of domination number. Sharp upper and lower bounds of Π1 and Π2 are given. In addition, the corresponding extreme graphs are characterized, and our conclusions enrich and extend some known results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:332:y:2018:i:c:p:338-350
    DOI: 10.1016/j.amc.2018.03.058
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Shaohui Wang & Zehui Shao & Jia-Bao Liu & Bing Wei, 2019. "The Bounds of Vertex Padmakar–Ivan Index on k -Trees," Mathematics, MDPI, vol. 7(4), pages 1-10, April.
    2. 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.
    3. Tomáš Vetrík & Selvaraj Balachandran, 2020. "General multiplicative Zagreb indices of trees and unicyclic graphs with given matching number," Journal of Combinatorial Optimization, Springer, vol. 40(4), pages 953-973, November.
    4. Fang Gao & Xiaoxin Li & Kai Zhou & Jia-Bao Liu, 2018. "The Extremal Graphs of Some Topological Indices with Given Vertex k -Partiteness," Mathematics, MDPI, vol. 6(11), pages 1-11, November.
    5. Shaohui Wang & Chunxiang Wang & Lin Chen & Jia-Bao Liu & Zehui Shao, 2018. "Maximizing and Minimizing Multiplicative Zagreb Indices of Graphs Subject to Given Number of Cut Edges," Mathematics, MDPI, vol. 6(11), pages 1-10, October.

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