Abstract
This study delves into the mathematical concepts and applications of Zagreb Indices, graph theory-based descriptors, in the realm of chemoinformatics. Focusing on key indices, Zg(1) and Zg(2), which quantify the sum of vertex degrees and the sum of squared vertex degrees, respectively, the research provides a comprehensive overview of their historical development and multifaceted applications. A systematic review of literature underscores their relevance in quantitative structure-activity relationship (QSAR) modeling, drug discovery, materials science, and environmental impact assessment. Mathematical formulations are presented, emphasizing their significance as topological descriptors for molecular structures. The study identifies challenges, such as graph isomorphism sensitivity and the need for dynamic descriptors, prompting the proposal of future directions. Potential advancements include integration with machine learning, the development of dynamic Zagreb Indices, and exploration of quantum mechanical extensions. The paper concludes with a call to action for researchers to contribute to the ongoing evolution of Zagreb Indices, recognizing their potential impact on drug discovery, materials science, and beyond.