Modeling benzene physicochemical properties using Zagreb upsilon indices

Abstract Quantitative structure–property relationship (QSPR) frameworks leverage topological indices to model the physicochemical attributes of molecular structures. In this study, we introduce the concept of upsilon degree and define the Zagreb upsilon indices based on this concept. Our findings demonstrate that the second Zagreb upsilon index exhibits the highest predictive accuracy for the π–electron energy of benzenes, surpassing existing degree-based topological indices with correlation coefficients exceeding 0.93. This accuracy was measured using statistical correlation analysis, and a direct comparison with the Randić and geometric-arithmetic indices further supports the superior performance of the second Zagreb upsilon index. Furthermore, structural sensitivity and abruptness analyses, which assess the stability and variation of an index across different molecular structures, indicate that Zagreb upsilon indices offer superior performance compared to alternative indices. These results suggest that Zagreb upsilon indices have significant potential as a new and effective tool for QSPR research.