A novel tilted Sombor topological descriptor for improved QSPR analysis of hydrocarbon-based compounds using machine learning
Sadia Noureen, Nazma Ashraf, Asma Abbas Hassan Elnour, Majid Hussain, Maira Kiran, Adnan Aslam, Keneni Abera Tola · Scientific Reports · 2026
This study introduces a new topological descriptor “Tilted Sombor index (TSO)”, designed using a novel approach that incorporates the graph’s radius along with the eccentricity and degree of its vertices. To evaluate its applicability, the descriptor was computed for a data set of 332 hydrocarbon-based molecular structures and examined through quantitative structure-property relationship analysis. Linear and logarithmic regression approaches were first employed to analyze the correlation between the proposed index and several physicochemical properties. To integrate the study with machine learning approach, the Random Forest and XGBoost models were then implemented to model nonlinear patterns and improve predictive accuracy. The analysis indicates that the tilted Sombor index performs better than the classical Sombor index for most of the investigated properties. The strongest predictions were observed for heavy atom count and molecular weight, where the Random Forest model produced a coefficient of determination close to \(R^2 \approx 0.9992\) . Training-testing procedures together with cross-validation analysis confirmed the consistency and reliability of the developed predictive models. These findings suggest that the proposed index is an effective molecular descriptor for QSPR studies and has useful applications in chemical graph theory and molecular property prediction.