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Analysis of Wiener and Hyper-Wiener Indices in Generalized R-Vertex Corona and Join Graphs of Diameter at Most Three

Author

Listed:
  • Vimal M.
  • Md. Ashraful Alam
  • Kalaimurugan G.
  • Vinnarasi L.

Abstract

Among various graph products, the corona product continues to inspire novel research. Subdivision graphs play a key role in understanding graph behaviour under edge modifications. The estimation of Wiener index under various graph operations is of considerable importance and has attracted substantial attention in chemical graph theory. In this paper, we determine the eccentricity of each vertex within the intricate structures of R-graphs. With its aid, we establish strict bounds for the Wiener index for the generalized R-vertex corona of graphs with diameter at most 3 and the Wiener index for the generalized R-vertex and edge join of graphs with diameter at most 3. We have also derived the hyper-Wiener index expression, reflecting its growing relevance across various emerging and rapidly advancing fields.

Suggested Citation

  • Vimal M. & Md. Ashraful Alam & Kalaimurugan G. & Vinnarasi L., 2026. "Analysis of Wiener and Hyper-Wiener Indices in Generalized R-Vertex Corona and Join Graphs of Diameter at Most Three," Journal of Mathematics, Hindawi, vol. 2026, pages 1-17, March.
    • Handle: RePEc:hin:jjmath:9280105
    DOI: 10.1155/jom/9280105
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