Machine Learning Prediction of Graph Invariants Using Zagreb-Type, Polynomial, and Adriatic Indices

Topological indices (TIs) are essential tools for recording molecular networks and graphs structural information. These include Zagreb-type indices, Zagreb polynomials, and Misbalance Adriatic indices, which efficiently reflect both local irregularity and global degree distribution. In order to forecast computationally difficult graph invariants, such as chromatic number, graph energy, diameter, independence number, and assortativity, we present a unified machine learning (ML) framework in this work that makes use of these sophisticated degree-based descriptors. More than 50 topological features are added to a dataset of 10,000 synthetic and real-world chemical graphs. Five-fold cross validation is used to assess several regression models, including Random Forest, Gradient Boosting (XGBoost, LightGBM), Support Vector Regression, Artificial Neural Networks, and KNN. According to experimental findings, gradient boosting models perform best overall, with XGBoost achieving an R2 value for graph energy prediction of up to 0.94. Zagreb polynomial coefficients and quadratic Misbalance Adriatic indices are among the most important characteristics, especially for irregular graphs, according to SHAP-based explainability. The findings show that an efficient approximation paradigm for challenging graph invariants can be obtained by combining sophisticated degree-based and polynomial descriptors with machine learning.