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On Bond Incident Degree Indices of Chemical Graphs

Author

Listed:
  • Abeer M. Albalahi

    (Department of Mathematics, College of Science, University of Ha’il, Ha’il P.O. Box 2440, Saudi Arabia)

  • Akbar Ali

    (Department of Mathematics, College of Science, University of Ha’il, Ha’il P.O. Box 2440, Saudi Arabia)

  • Zhibin Du

    (School of Software, South China Normal University, Foshan 528225, China)

  • Akhlaq Ahmad Bhatti

    (Department of Sciences and Humanities, National University of Computer and Emerging Sciences, Lahore Campus, B-Block, Faisal Town, Lahore 54770, Pakistan)

  • Tariq Alraqad

    (Department of Mathematics, College of Science, University of Ha’il, Ha’il P.O. Box 2440, Saudi Arabia)

  • Naveed Iqbal

    (Department of Mathematics, College of Science, University of Ha’il, Ha’il P.O. Box 2440, Saudi Arabia)

  • Amjad E. Hamza

    (Department of Mathematics, College of Science, University of Ha’il, Ha’il P.O. Box 2440, Saudi Arabia)

Abstract

By swapping out atoms for vertices and bonds for edges, a graph may be used to model any molecular structure. A graph G is considered to be a chemical graph in graph theory if no vertex of G has a degree of 5 or greater. The bond incident degree (BID) index for a chemical graph G is defined as the total of contributions f ( d G ( u ) , d G ( v ) ) from all edges u v of G , where d G ( w ) stands for the degree of a vertex w of G , E ( G ) is the set of edges of G , and f is a real-valued symmetric function. This paper addresses the problem of finding graphs with extremum BID indices over the class of all chemical graphs of a fixed number of edges and vertices.

Suggested Citation

  • Abeer M. Albalahi & Akbar Ali & Zhibin Du & Akhlaq Ahmad Bhatti & Tariq Alraqad & Naveed Iqbal & Amjad E. Hamza, 2022. "On Bond Incident Degree Indices of Chemical Graphs," Mathematics, MDPI, vol. 11(1), pages 1-13, December.
    • Handle: RePEc:gam:jmathe:v:11:y:2022:i:1:p:27-:d:1010272
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    References listed on IDEAS

    as
    1. Ali, Akbar & Raza, Zahid & Bhatti, Akhlaq Ahmad, 2016. "Bond incident degree (BID) indices of polyomino chains: A unified approach," Applied Mathematics and Computation, Elsevier, vol. 287, pages 28-37.
    2. Yongsheng Rao & Adnan Aslam & Muhammad Unfowan Noor & A. Othman Almatroud & Zehui Shao, 2020. "Bond Incident Degree Indices of Catacondensed Pentagonal Systems," Complexity, Hindawi, vol. 2020, pages 1-7, August.
    3. Muhammad Rizwan & Akhlaq Ahmad Bhatti & Muhammad Javaid & Fahd Jarad, 2021. "Some Bounds on Bond Incident Degree Indices with Some Parameters," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-10, July.
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