Degree-based Topological Characterization and Graph Energy Prediction of Silicon Carbide Network Si2C3-I[k, l] via Double Graph Operator

This study presents the precise formulation of the Nirmala index and the first and second inverse Nirmala indices for the double graph of the silicon carbide network Si2C3-I[k, l], using its M-polynomial. Entropy measures based on these indices are derived using Shannon's entropy model. Numerical and graphical comparisons are conducted between the Nirmala indices and their corresponding entropy measures. Curve fitting and Pearson correlation analysis are used to examine their relationships. Finally, the computed indices are employed to develop a predictive model for the graph energy of Si2C3-I[k, l] and estimate the HOMO-LUMO gap.