Investigation of resolving sets in the molecular structures of hypoglycemia medications

In drug structure research, distance-based parameters are essential as they enable graph representations to accurately identify and characterize chemical structures. This approach provides a more comprehensive understanding of molecular characteristics and behavior. Within graph theory, a resolving set is a subset of vertices where each vertex in the graph is uniquely identified by its distance vector to the vertices in this set. The metric dimension is the minimum size of such a resolving set. In pharmaceutical research, the metric dimension serves as a valuable measure of structural similarity and difference between molecules. This paper discusses the metric dimensions of several classes of oral hypoglycemic medication compounds, including sulfonylureas, meglitinides, biguanides, thiazolidinediones, \(\alpha\)-glucosidase inhibitors, DPP-4 inhibitors, SGLT2 inhibitors, and cycloset. Our analysis confirms that each of these molecular graphs possesses a unique metric dimension, signifying their structural distinctness. While some drugs share the same metric dimension, others exhibit significant differences that distinguish them despite structural similarities. These variations in metric dimension enhance the effectiveness and accuracy of molecular structure identification, establishing it as a powerful parameter in graph-based pharmaceutical research.