Degree-Based Topological Entropies of Polythiophene and Bipolaron Networks: Exact Formulas and Descriptor Redundancy

Abstract

Degree-based graph entropies quantify structural heterogeneity in molecular networks. However, a unified entropy treatment of polythiophene and its bipolaron counterpart, together with a direct assessment of descriptor redundancy, is still lacking. This study therefore derives closed-form expressions for fourteen degree-based topological indices and their Shannon-type entropies for polythiophene PLP and the bipolaron network BIPLP, and examines whether the resulting entropy measures provide distinct structural information. The descriptors considered are the Zagreb, hyper-Zagreb, forgotten, Yemen, redefined Zagreb, Randi´c, Sombor, Yemen–Sombor, general sum-connectivity, geometric–arithmetic, and atom–bond connectivity indices. The edge partitions are determined from the degrees of adjacent vertices and then used to obtain formulas for all admissible values of p. Numerical values and plots show how the indices and entropies vary with p. The entropy sequences are highly correlated over the examined ranges, indicating that several descriptors carry nearly the same information. The formulas give exact structural invariants for the two network families and help identify a smaller, non-redundant descriptor set for later structure–property studies.