An Effective Approach Based on the Malatya Centrality Algorithm for Determining the Maximum Independent Set and Minimum Vertex Cover in Molecular Graphs

Molecular graphs are graphs formed by considering atoms as nodes and the connections between these atoms as edges, which constitute the structure of chemical compounds. These graphs are used to analyze the chemical and structural properties of molecules. In this study, an effective and robust approach based on the Malatya Centrality algorithm is proposed for determining the maximum independent set and the minimum vertex cover in molecular graphs. In the proposed approach, the molecular graph is transformed into a graph structure consisting of nodes and edges. Subsequently, Malatya centrality values are computed for the nodes in this graph. Using these values, the maximum independent set is first calculated for the molecular graph. Then, utilizing this set, the minimum vertex cover for the molecular graph is determined. To demonstrate the effectiveness of the proposed approach, tests and analyses were conducted on molecular graphs of various sizes, complexities, and classes. The successful test results and analyses indicate that the proposed approach is an effective and robust method for determining the maximum independent set and the minimum vertex cover in molecular graphs.