This chapter offers a novel method for using graph theoryGraph theory andMachine Learning (ML) machine learningGraph-based learning (ML) to analyze monomer structuresMonomer structures. We selected 40 monomer structuresMonomer structures from two different polymer classes namely aromatic and aliphatic polymersAliphatic polymers and converted them into molecular graphsMolecular graphs, and evaluated 10 topological indicesTopological indices based on distanceDistance-based indices measures. Our primary objective was to classify these monomers into aliphatic and aromatic polymersAromatic polymers using MLMachine Learning (ML) models. We generated input data for the MLMachine Learning (ML) classification task by converting the molecular graphsMolecular graphs into vector representationsVector representations. Additionally, we discuss the broader relevance of graph theoryGraph theory, including its application in ECG data classificationECG data classification using visibility graphsVisibility graphs. This chapter highlights the possibility of using MLMachine Learning (ML) approaches to graph theoryGraph theory for sophisticated chemical research and other scientific applications.