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On‐Bond Incident Degree Indices of Square‐Hexagonal Chains

Author

Listed:
  • Tariq A. Alraqad
  • Hicham Saber
  • Akbar Ali
  • Jaya Percival Mazorodze

Abstract

For a graph G, its bond incident degree (BID) index is defined as the sum of the contributions f(du, dv) over all edges uv of G, where dw denotes the degree of a vertex w of G and f is a real‐valued symmetric function. If f(du, dv) = du + dv or dudv, then the corresponding BID index is known as the first Zagreb index M1 or the second Zagreb index M2, respectively. The class of square‐hexagonal chains is a subclass of the class of molecular graphs of minimum degree 2. (Formal definition of a square‐hexagonal chain is given in the Introduction section). The present study is motivated from the paper (C. Xiao, H. Chen, Discrete Math. 339 (2016) 506–510) concerning square‐hexagonal chains. In the present paper, a general expression for calculating any BID index of square‐hexagonal chains is derived. The chains attaining the maximum or minimum values of M1 and M2 are also characterized from the class of all square‐hexagonal chains having a fixed number of polygons.

Suggested Citation

  • Tariq A. Alraqad & Hicham Saber & Akbar Ali & Jaya Percival Mazorodze, 2022. "On‐Bond Incident Degree Indices of Square‐Hexagonal Chains," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:1864828
    DOI: 10.1155/2022/1864828
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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.
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