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On Bond Incident Degree Indices of Fixed-Size Bicyclic Graphs with Given Matching Number

Author

Listed:
  • Akbar Ali

    (Department of Mathematics, College of Science, University of Ha’il, Ha’il 81451, Saudi Arabia)

  • Abeer M. Albalahi

    (Department of Mathematics, College of Science, University of Ha’il, Ha’il 81451, Saudi Arabia)

  • Abdulaziz M. Alanazi

    (Department of Mathematics, Faculty of Sciences, University of Tabuk, Tabuk P.O. Box 741, Saudi Arabia)

  • Akhlaq A. Bhatti

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

  • Tariq Alraqad

    (Department of Mathematics, College of Science, University of Ha’il, Ha’il 81451, Saudi Arabia)

  • Hicham Saber

    (Department of Mathematics, College of Science, University of Ha’il, Ha’il 81451, Saudi Arabia)

  • Adel A. Attiya

    (Department of Mathematics, College of Science, University of Ha’il, Ha’il 81451, Saudi Arabia)

Abstract

A connected graph with p vertices and q edges satisfying q = p + 1 is referred to as a bicyclic graph. This paper is concerned with an optimal study of the BID (bond incident degree) indices of fixed-size bicyclic graphs with a given matching number. Here, a BID index of a graph G is the number BID f ( G ) = ∑ v w ∈ E ( G ) f ( d G ( v ) , d G ( w ) ) , where E ( G ) represents G ’s edge set, d G ( v ) denotes vertex v ’s degree, and f is a real-valued symmetric function defined on the Cartesian square of the set of all different members of G ’s degree sequence. Our results cover several existing indices, including the Sombor index and symmetric division deg index.

Suggested Citation

  • Akbar Ali & Abeer M. Albalahi & Abdulaziz M. Alanazi & Akhlaq A. Bhatti & Tariq Alraqad & Hicham Saber & Adel A. Attiya, 2024. "On Bond Incident Degree Indices of Fixed-Size Bicyclic Graphs with Given Matching Number," Mathematics, MDPI, vol. 12(23), pages 1-14, December.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:23:p:3806-:d:1534453
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    References listed on IDEAS

    as
    1. Shang, Yilun, 2022. "Sombor index and degree-related properties of simplicial networks," Applied Mathematics and Computation, Elsevier, vol. 419(C).
    2. Zheng, Ruiling & Su, Peifeng & Jin, Xian’an, 2023. "Arithmetic-geometric matrix of graphs and its applications," Applied Mathematics and Computation, Elsevier, vol. 442(C).
    Full references (including those not matched with items on IDEAS)

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