Relationship of Graph Energies with Some Graph Features

Topological indices are widely used for identifying structure-property relationships due to their computational simplicity. Graph energies are an active research area nowadays, with over a thousand publications and an average of two papers published weekly. This study has two parts. The first part aims to explore the relationship between various graph energies of random tree graphs and well-known graph structural features, and the second part utilizes energies to predict the physicochemical properties of real-world molecular graphs. For both studies, we used XGBoost and SHAP (SHapley Additive Explanations) to build a decision-making model. We employed the Randomised Search CV to enhance XGBoost's performance further. This algorithm randomly selects a set of hyperparameters and evaluates the model's performance using cross-validation, resulting in improved accuracy. According to our research, XGBoost and SHAP (SHapley Additive Explanations) can help examine the relationships between topological indices and the structural features and physicochemical properties of drug molecules.