Detour Eccentric Sum Index for QSPR Modeling in Molecular Structures

In this paper, we study the detour eccentric sum index (DESI) to obtain the Quantitative Structure–Property Relationship (QSPR) for different molecular structures. We establish theoretical bounds for this index and compute its values across fundamental graph families. Through correlation analyses between the physicochemical properties of molecular structures representing anti-malarial and breast cancer drugs, we show the high predictive value of two topological parameters, detour diameter (DD) and detour radius (DR). Specifically, DR shows strong positive correlations with boiling point, enthalpy, and flash point (up to 0.94), while DD is highly correlated with properties such as molar volume, molar refraction, and polarizability (up to 0.97). The DESI was then selected for detailed curvilinear regression modeling and comparison against the established eccentric distance sum index. For anti-malarial drugs, the second-order model yields the best fit. The DESI provides optimal prediction for boiling point, enthalpy, and flash point. In breast cancer drugs, the second-order model is again favored for properties except for melting point, best described by a third-order model. The results highlight how well the index captures subtle structural characteristics.