An Investigation into Non Simple Molecular Graph Modeling Of Chemical Structures Using Topological Indices and Graph Energy with Statistical Approaches

Abstract

Graph theory models real-world systems, using vertices and edges to represent components newlineand their connections. In chemical graph theory, this applies to molecular structures, newlinewhere atoms are vertices and bonds are edges. The study of molecular graphs through newlinetopological indices and graph energy has advanced the understanding of chemical newlinestructures and behavior without experiments. This thesis models chemical structures newlineas non-simple molecular graphs, focusing on self-loops, multigraphs and pseudographs. newlineEarly chapters examine the spectrum, energy, and Laplacian energy of complete graphs, newlinestar graphs, and coalescence of complete graphs with loops, offering a mathematical newlineframework to analyze complex molecular structures and their relation to physicochemical newlineand biological properties, aiding drug development. newlineWe use multigraph-based curvilinear regression with Revan indices to analyze newlinecardiovascular drugs, improving predictions of drug efficacy. A QSPR/QSAR analysis newlineof antiviral drugs employs topological indices and multiple linear regression to model newlineeffectiveness against COVID-19. This approach extends to antipsychotic drugs, utilizing newlinemultigraph modeling and advanced statistical techniques to predict physicochemical newlineproperties, with a focus on heteroatoms in modeling for greater accuracy. Lastly, total newlinequadratic indices are applied to non-steroidal anti-inflammatory drugs (NSAIDs), modeled newlineas pseudographs with weighting schemes, to predict their physicochemical properties newline