A comprehensive study on topological indices and entropy measures for terbium niobate using logarithmic regression models

In this article, we establish a detailed mathematical investigation of the molecular graph of terbium niobate (TbNbO₄) from a chemical graph theory point of view. A series of degree-based topological indices, such as Randić, ABC, GA, Zagreb, and their redefined versions, are calculated to define molecular structure. In addition, related entropy values from these indices are found to determine structural complexity and information content. Numerical and graphical studies illustrate how indices and entropies are related to molecular size, showing unique growth trends and sensitivities. Logarithmic SPSS regression models are formulated to investigate how topological indices are related to entropy measures, providing significant correlations. The findings show how various indices are complementary to each other in representing local and global structures and are useful in molecular characterization, drug discovery, and computational chemistry.