Graph applications in Taxicab geometry

This thesis examines the properties of conic sections within the context of Taxicab geometry, focusing on the graph structures that emerge from these properties. The study is organized into five chapters. The first chapter presents an overview of the history of graph theory and Taxicab geometry. The second chapter introduces fundamental concepts and various types of graphs in graph theory. In the third chapter, definitions and characteristics of conic sections in the Taxicab plane are discussed, with comparisons made to their Euclidean counterparts. The fourth chapter integrates graphs with Taxicab geometry, modeling conic sections such as circles, ellipses, and hyperbolas. The necessary assumptions and mathematical proofs required for these models are also provided. To enhance the clarity of the study, illustrative examples and detailed proofs are included. The final chapter presents the conclusions and evaluation of the research.