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Some Bond Incident Degree Indices of Cactus Graphs

Author

Listed:
  • Akbar Ali
  • Akhlaq Ahmad Bhatti
  • Naveed Iqbal
  • Tariq Alraqad
  • Jaya Percival Mazorodze
  • Hicham Saber
  • Abdulaziz M. Alanazi

Abstract

A connected graph in which no edge lies on more than one cycle is called a cactus graph (also known as Husimi tree). A bond incident degree (BID) index of a graph G is defined as ∑uv∈E(G)f(dG(u), dG(v)), where dG(w) denotes the degree of a vertex w of G, E(G) is the edge set of G, and f is a real‐valued symmetric function. This study involves extremal results of cactus graphs concerning the following type of the BID indices: IfiG=∑uv∈EGfidGu/dGu+fidGv/dGv, where i ∈ {1,2}, f1 is a strictly convex function, and f2 is a strictly concave function. More precisely, graphs attaining the minimum and maximum Ifi values are studied in the class of all cactus graphs with a given number of vertices and cycles. The obtained results cover several well‐known indices including the general zeroth‐order Randić index, multiplicative first and second Zagreb indices, and variable sum exdeg index.

Suggested Citation

  • Akbar Ali & Akhlaq Ahmad Bhatti & Naveed Iqbal & Tariq Alraqad & Jaya Percival Mazorodze & Hicham Saber & Abdulaziz M. Alanazi, 2022. "Some Bond Incident Degree Indices of Cactus Graphs," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:8325139
    DOI: 10.1155/2022/8325139
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    References listed on IDEAS

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    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.
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