Edge Resolvability of Certain Chemical Compounds used in Hepatitis-C treatment

Abstract

The representation of molecules by graphs, where the vertices and edges of the graphs are the atoms and the valence bonds between a pair of atoms, respectively, is the most successful use of graph theory in chemistry. Graph theory encompasses various parameters, with the dimension of edge metric being a distinct and significant parameter. The edge metric dimension is a fundamental concept in graph theory that extends the notion of metric dimension from vertices to edges. This notion involves selecting specific vertices, wherein each graph edge possesses a distinct location or identification. Resolving sets were specifically applied in pharmaceutical research to find patterns shared by several different drugs. Since very early times, medicinal drugs have played a significant part in human civilization. In this article, we study the edge metric dimension for the typical molecular structures of two important drugs namely pibrentasvir (P₈₀) and vancomycin (V₁₀₁).