Gutman index of transformation graphs

Graph theory is widely used in many areas. One of these areas is mathematical chemistry. Numerous topological indices have been studied in this area. The ones that are commonly used among these indices are the ones that are connected to degree and distance. Gutman index, which has a substantial role in mathematical chemistry, has been studied in this thesis. Gutman index is a topological index in which both degree and distance are used at the same time. This thesis consists of five chapters. In section 1, the way graph theory came forward and the fields in which the theory is used are referred. Information on the topological index are also given. In section 2, there are some definitions used in this thesis. In section 3, Gutman index, a topological index, which used in this thesis is analyzed. In addition, the definition of transformation graphs has been provided. In section 4, Gutman index is studied through some transformation graphs of path graph, cycle graph and star graph, and general formulas are obtained. In section 5, there are conclusions and hypotheses obtained from this study.