On Wiener index for generalized neighborhood corona of total graphs

Graph products have remained a vital area of exploration in graph theory, offering deep structural insights into complex networks. Among these, the corona product has emerged as a particularly versatile operation, especially when analyzed through the lens of subdivision graphs, which effectively capture structural modifications resulting from edge transformations. In this study, we focus on the generalized vertex neighborhood corona of total graphs with a diameter of at most 3. We establish tight bounds for the Wiener index of such graphs and provide a closed-form expression for the corresponding hyper-Wiener index. These distance-based topological indices play a crucial role in various applications, including network reliability assessment, epidemic spread modeling, molecular graph structural analysis, and spectral studies of graphs. The results presented contribute to a broader understanding of graph invariants under advanced graph operations and underscore their relevance across multiple scientific and engineering disciplines.