Wiener type topological indices of some special graphs

In graph theory, many topological indices have been defined to measure different topological properties. In this work, specially selected Wiener type distance-based topological indices, Wiener, Wiener polarity, Hyper Wiener, Harary, reciprocal complementary Wiener and terminal Wiener indices, are discussed. In the first chapter, information about the subject, purpose and method of the thesis is given. In the second chapter, some necessary basic information about graph theory, definitions of graph types used in this study and the most well-known distance-based topological indices of Wiener type are given. In the third part, the values of these indices for the well-known path graph 𝑃𝑛, complete graph 𝐾𝑛, cycle graph 𝐶𝑛 and star graph 𝑆1,𝑛 in the literature are recalculated depending on their orders to be used in this study. Then, by using this calculation, for the special graph types based on complete graphs such as pineapple graph, urchin graph, broken urchin graph, kite graph, double kite graph and complete caterpillar graph; for the special graph types based on cycle graphs such as turnip graph, lollipop graph and sun graphs and for some tree types such as double star graph and starlike tree, Wiener type topological indices are calculated and presented based on graph parameters. In the last section, which is the fourth section, the conclusions and suggestions made as a result of the thesis are mentioned.