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First General Zagreb Co‐Index of Graphs under Operations

Author

Listed:
  • Muhammad Javaid
  • Muhammad Ibraheem
  • Ebenezer Bonyah
  • Uzma Ahmad
  • Shaohui Wang

Abstract

Topological indices are graph‐theoretic parameters which are widely used in the subject of chemistry and computer science to predict the various chemical and structural properties of the graphs respectively. Let G be a graph; then, by performing subdivision‐related operations S, Q, R, and T on G, the four new graphs S(G) (subdivision graph), Q(G) (edge‐semitotal), R(G) (vertex‐semitotal), and T(G) (total graph) are obtained, respectively. Furthermore, for two simple connected graphs G and H, we define F‐sum graphs (denoted by G+FH) which are obtained by Cartesian product of F(G) and H, where F ∈ {S, R, Q, T}. In this study, we determine first general Zagreb co‐index of graphs under operations in the form of Zagreb indices and co‐indices of their basic graphs.

Suggested Citation

  • Muhammad Javaid & Muhammad Ibraheem & Ebenezer Bonyah & Uzma Ahmad & Shaohui Wang, 2022. "First General Zagreb Co‐Index of Graphs under Operations," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:5094929
    DOI: 10.1155/2022/5094929
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    References listed on IDEAS

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    1. Gutman, Ivan, 2017. "On coindices of graphs and their complements," Applied Mathematics and Computation, Elsevier, vol. 305(C), pages 161-165.
    2. Muhammad Javaid & Muhammad Ibraheem & Uzma Ahmad & Jia-Bao Liu & M.M. Bhatti, 2021. "Sharp Bounds of First Zagreb Coindex for F-Sum Graphs," Journal of Mathematics, Hindawi, vol. 2021, pages 1-19, October.
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