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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
  • M. T. Rahim

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∈EGfdGu,dGv, where dGw denotes the degree of a vertex w of G, EG 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 & M. T. Rahim, 2022. "Some Bond Incident Degree Indices of Cactus Graphs," Journal of Mathematics, Hindawi, vol. 2022, pages 1-5, January.
    • Handle: RePEc:hin:jjmath:8325139
    DOI: 10.1155/2022/8325139
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