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Abstract

The partition dimension of a graph in chemical graph theory refers to a graph invariant used to analyze the structural properties of molecules. It represents the minimum number of clusters or resolving partition set required to uniquely identify each vertex in the graph based on the neighborhoods within their respective clusters. In the context of chemical graph theory, the vertices of the graph correspond to atoms, and edges represent bonds between these atoms in a molecular structure. Determining the partition dimension of a chemical graph helps in understanding the relationships between molecular components and their spatial arrangements. It assists in the analysis of molecular conformations, structure-activity relationships, and drug design by identifying the smallest number of distinct clusters or resolving partition sets necessary to uniquely define the local environment of each atom in the molecule. The partition dimension is a valuable metric in computational chemistry, offering insights into molecular complexity, aiding in the prediction of molecular properties, and facilitating the discovery of new drug candidates with specific structural characteristics. In this work, we have calculated the partition dimension of certain ANTI-HIV drug molecular structures.

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