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Analysis of the Wiener Index for Graph Families Generated by Subdivision-Based Double Join and Double Corona Products

Author

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  • M. Vimal
  • Md. Ashraful Alam
  • G. Kalaimurugan

Abstract

Among the diverse types of graph products, the double join and double corona operations have remained central to many recent developments in graph theory, offering fresh insights and problem-solving strategies. Subdivision graphs, in particular, serve as an essential tool for examining how structural modifications along edges influence the overall properties of a graph. In this study, we present analytical expressions for the Wiener index of the generalized subdivision double join of graphs defined on finite-dimensional vector spaces with diameter at most two. Building on this result, the corresponding formula for the hyper-Wiener index is also derived. Furthermore, a tight bound for the Wiener index of the generalized subdivision double corona product is established. The outcomes of this study possess potential applications in the analysis of multilayer perceptron (MLP) structures, an important class of artificial neural networks that efficiently address complex computational tasks through adaptive learning mechanisms.

Suggested Citation

  • M. Vimal & Md. Ashraful Alam & G. Kalaimurugan, 2026. "Analysis of the Wiener Index for Graph Families Generated by Subdivision-Based Double Join and Double Corona Products," Journal of Applied Mathematics, Hindawi, vol. 2026, pages 1-11, June.
    • Handle: RePEc:hin:jnljam:4882892
    DOI: 10.1155/jama/4882892
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