**Thesis Type:** Postgraduate

**Institution Of The Thesis:** Uludağ Üniversitesi, Turkey

**Approval Date:** 2016

**Thesis Language:** Turkish

**Student:** ŞEYMA ÖZÖN YILDIRIM

**Supervisor: **İSMAİL NACİ CANGÜL

Topological indices are constants which have a lot of applications mainly in Chemistry. For the first time, they were started to be defined in 1940s, and by the technological advances in computer technologyi they are now preferred to previously used methods. A lot of topological indices are defined for this reason. These indices are mostly defined in terms of vertex degrees, distances or matrices corresponding to graphs. The aim of this work is to consider 11 frequently used topological indices and calculate these indices for some well-known graph classes, to obtain fornulae for them and to find the integer and prime values of these indices. This thesis consists of three chapters. The first chapter is the Introduction. Here, we give the definition of a graph, their history, some special graphs and their properties, the graph indices under consideration, and some newly defined graph types. These will be used throughout the thesis. In the second chapter, calculations of 11 graph indices for some widely-used graph classes are given. Finally in the third chapter, the integer and prime values of these indices are determined.