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

Vimal M., Md. Ashraful Alam, Kalaimurugan G. and Vinnarasi L.

Journal of Mathematics, 2026, vol. 2026, 1-17

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.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:9280105

DOI: 10.1155/jom/9280105

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