The graph parameters for graphs of twist knots

This thesis study deals with a study that combines the fields of graph theory and knot theory. Here, the graph parameters of the twist knots, which is an important knot family, are examined. First of all, graphs of twist knots were obtained by coloring method and then the basic graph parameters known for these graphs were examined. Generalizations have been made based on these calculations. In the study process, the methods and techniques in graph theory were utilized to a great extent. In the introduction part of the thesis; the roots of the relationship between knot theory and graph theory and the point where the idea of knot graph has reached today since its first emergence are mentioned. In addition, the importance of the studied problem in terms of literature is also discussed in this section. In the second part, the basic concepts and notations that guide the studies are defined. In the third chapter, the material of the study and the method of obtaining it are given. In the fourth chapter, the obtained results are given and generalizations of the graph parameters of the graphs of twist knots are presented with their proofs. In the last section, these results and generalizations are emphasized and their effects and importance are discussed.