Vertex-Edge Weighted Molecular Graphs: A study on topological indices and their relevance to physicochemical properties of drugs in use cancer treatment

Abstract: Quantitative Structure-Property Relationship (QSPR) analysis plays a crucial role in predicting physicochemical properties and biological activities of pharmaceutical compounds, aiding in drug design and optimization. This study focuses on leveraging QSPR within the framework of vertex and edge weighted (VEW) molecular graphs, exploring their significance in drug research. By examining 48 drugs in used in the treatment of various cancers and their physicochemical properties, previous studies serve as a foundation for our research. Introducing a novel methodology for computing vertex and edge weights, exemplified by the drug Busulfan, we highlight the importance of considering atomic properties and inter-bond dynamics. Statistical analysis, employing linear regression models, reveals enhanced correlations between topological indices and physicochemical properties of drugs. Comparison with previous studies on unweighted molecular graphs highlights the enhancements achieved with our approach.