Asian Journal of Research and Reviews in Physics

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 PL_P and the bipolaron network BIPL_P, 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.