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Fixed-Order Chemical Trees with Given Segments and Their Maximum Multiplicative Sum Zagreb Index

Author

Listed:
  • Akbar Ali

    (Department of Mathematics, College of Science, University of Ha’il, Ha’il P.O. Box 2240, Saudi Arabia)

  • Sadia Noureen

    (Department of Mathematics, Faculty of Science, University of Gujrat, Gujrat 50700, Pakistan)

  • Abdul Moeed

    (Department of Mathematics, Faculty of Science, University of Gujrat, Gujrat 50700, Pakistan)

  • Naveed Iqbal

    (Department of Mathematics, College of Science, University of Ha’il, Ha’il P.O. Box 2240, Saudi Arabia)

  • Taher S. Hassan

    (Department of Mathematics, College of Science, University of Ha’il, Ha’il P.O. Box 2240, Saudi Arabia
    Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy
    Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt)

Abstract

Topological indices are often used to predict the physicochemical properties of molecules. The multiplicative sum Zagreb index is one of the multiplicative versions of the Zagreb indices, which belong to the class of most-examined topological indices. For a graph G with edge set E = { e 1 , e 2 , ⋯ , e m } , its multiplicative sum Zagreb index is defined as the product of the numbers D ( e 1 ) , D ( e 2 ) , ⋯ , D ( e m ) , where D ( e i ) is the sum of the degrees of the end vertices of e i . A chemical tree is a tree of maximum degree at most 4. In this research work, graphs possessing the maximum multiplicative sum Zagreb index are determined from the class of chemical trees with a given order and fixed number of segments. The values of the multiplicative sum Zagreb index of the obtained extremal trees are also obtained.

Suggested Citation

  • Akbar Ali & Sadia Noureen & Abdul Moeed & Naveed Iqbal & Taher S. Hassan, 2024. "Fixed-Order Chemical Trees with Given Segments and Their Maximum Multiplicative Sum Zagreb Index," Mathematics, MDPI, vol. 12(8), pages 1-19, April.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:8:p:1259-:d:1379845
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    References listed on IDEAS

    as
    1. Lkhagva Buyantogtokh & Batmend Horoldagva & Kinkar Chandra Das, 2020. "On reduced second Zagreb index," Journal of Combinatorial Optimization, Springer, vol. 39(3), pages 776-791, April.
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