Topological indices of graphs and chemical applications

Graph Theory, as a branch of mathematics, allows us to analyze vertices and the relationships (edges) between vertices. This theory is one of the most dynamic and applicable branches of mathematics. Graph applications have made significant progress in the last two decades. One of the most important applications in this field is "Chemical Graph Theory", also known as "Molecular Graph Theory", which has made significant contributions to the science of chemistry. Chemical graph theory has extended the mathematical framework deep into chemistry and has been a key to exploring the complexity of the molecular world. In chemical science, various properties such as physical, chemical and biological activities can be analyzed using chemical applications of graph theory. In the second chapter of this thesis, graph theoretic invariants, topological indices and QSPR/QSAR analysis of chemical graphs are extensively discussed. In the third chapter, the foundation for the fifth chapter is laid by discussing the QSPR/QSAR analysis of some cancer drugs. In the fourth chapter, original results were obtained by calculating the topological indices of some polysaccharides (chitin, chitosan and cellulose). In the fifth chapter, the molecular graphs of some cancer drugs were weighted and analyzed by QSPR/QSAR and the results were expressed. The sixth section consists of a brief review, a comparison of the findings, an explanation of open problems and a statement of observations.