Computing the Edge Metric Dimension of the Line Graph of the Molecular Graphs of Some Classes of Antiviral Drugs, with Focus on Mpox Treatments

Abstract

The study of viral infections, particularly those caused by monkeypox (Mpox), is crucial due to its significant public health impact and awareness. Graph theory, which is instrumental in understanding the topology of networks in various disciplines, is applied to studying antiviral drug structures to explore these antiviral drugs' structural and physicochemical properties using invariants such as metric dimension and edge metric dimension. These invariants offer insights into their mechanisms of action and potential for developing more effective therapies. The edge metric dimension is a graph theoretical parameter or invariant that allows for uniquely identifying all edges in a graph or bonds in a molecular graph through a chosen subset of vertices or atoms in a molecular graph, known as the edge resolving set. Line graphs can be applied in chemistry (modeling molecular structures), network theory, and computer science to solve problems like edge coloring and matching. In this paper, we specifically focus on the concept of edge metric dimension in a line graph of antiviral drug structures, which allows for the distinct identification of edges of their corresponding antiviral drug structures through the use of edge-resolving sets. This approach and results obtained not only enhances our knowledge and understanding of molecular interactions but also supports the advancement of effective therapeutic solutions in response to emerging health challenges such as Mpox disease. The following antiviral drug structures, namely Acyclovir, Brincidofovir, Cidofovir, Famciclovir, Tecovirimat, and Valacyclovir, are investigated in this study.