In the realm of chemical graph theory, a topological index is a numerical parameter derived from a molecular graph. This index offers a streamlined approach to numerically calculate and compare various physico-chemical properties of chemical compounds, such as melting point, boiling point, viscosity, size, shape, atom count, bond strength, enthalpy, and geometric characteristics. Traditional scientific exploration of these properties, conducted in a laboratory setting, is often timeintensive, costly, and demands expertise in the respective field. Chemical graph theory provides a more cost-effective and straightforward solution, enabling the correlation of topological indices with chemistry. This approach allows for the computational analysis of any chemical species using mathematical tools, circumventing the need for laboratory-based experiments. This approach offers considerable benefits in chemical science, as it employs mathematical and theoretical methods to estimate a molecule's physico-chemical properties. The primary objective of this paper is to elucidate the correlation between thorn graphs and topological indices, utilizing the methods of vertex degrees and edge partitioning. The paper conducts a rigorous analysis of thorn graphs using mathematical calculations, deriving the relationship between the indices. These indices play a pivotal role in a diverse array of research areas, including chemoinformatics, pharmaceutical industry applications, and toxicity prediction among others.