Exploring the Distance-Based Topological Indices for Total Graphs via Numerical Comparison

Graph theory serves as a valuable tool across numerous scientific disciplines, offering the means to model and analyze intricate networks. In this study, we explore the application of distance-based topological indices to a variety of graphs, including the total graph of paths, cycles, complete graphs, wheel graphs, helm graphs, and the Cartesian product of K₁ and K_n. We investigate five distance-based indices: the Wiener index, multiplicative Wiener index, hyper-Wiener index, Harary index, and average distance. Through detailed analysis, we derive general formulas for these indices and test them on the specified graphs. Using MATLAB for numerical comparisons, we demonstrate the effectiveness of these indices in capturing the structural properties of different graph types. The findings from this study enhance our understanding of topological indices and their applications within the field of graph theory.