Exploring entropy measures in polymer graphs using logarithmic regression model

Graph Entropies, calculated from indices, quantify the structural information of chemical linkages and graphs using Shannon's Entropy notion. This study investigates the chemical structures of polyester and polycarbonate polymers. Polyesters are synthetic polymers consisting of repeating chemical units linked by covalent bonds formed through ester groups. They are versatile materials found in a wide range of everyday products. In contrast, polycarbonates are thermoplastic polymers characterized by carbonate groups. Renowned for their strength and toughness, polycarbonates are widely used in engineering applications. In this study, we compute the Zagreb indices, redefined Zagreb indices, atom-bond connectivity index, and geometric-arithmetic index for polymer structures using edge partitioning based on degrees. Furthermore, we calculate Entropy measures for these structures using Shannon's Entropy notion. Through numerical computations, we compare the topological indices with their corresponding Entropy measures. Finally, we employ a regression model to analyze the relationship between these topological indices and Entropy metrics.