**Thesis Type:** Postgraduate

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

**Approval Date:** 2015

**Thesis Language:** Turkish

**Student:** UTKUM ŞANLI

**Supervisor: **İSMAİL NACİ CANGÜL

The main aim of this work is to recall several graph types, to calculate chromatic numbers and chromatic polynomials corresponding to these graphs, and to find some better and faster methods to calculate chromatic polynomials. This thesis consists of three chapters. In the first chapter, the fundamental definitions and results are recalled. Definition of graph and related notions, some brief history of graph theory, applications of graph theory, several graph types and their related properties are given. In the second chapter, colouring of graphs and some calculations used for this operation are given. In the third chapter, some new deletion results are given to help finding an easier method to calculate chromatic polynomial of a given graph. All the results obtained in this chapter are original results obtained in this thesis.