Computing The First Zagreb Index, The Wiener Index and The Gutman Index of The Power of Dihedral Group Using Python

This paper presents a computational study on three classical topological indices—the First Zagreb Index, Wiener Index, and Gutman Index—within the context of power graphs of the dihedral group , where is a positive integer representing half the order of the group. These indices are fundamental in mathematical chemistry and graph theory, serving as quantitative descriptors of graph structure and connectivity. The methodology involves constructing power graphs derived from and calculating the indices using Python programming, supported by the NetworkX, Matplotlib, and Gradio libraries. Numerical simulations were conducted for varying values of , revealing consistent algebraic patterns and insights into the structural complexity of the corresponding graphs. Additionally, an interactive Python-based interface is developed to facilitate real-time computation and visualization, thus promoting further exploration and application in algebraic graph theory