**Thesis Type:** Postgraduate

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

**Approval Date:** 2015

**Thesis Language:** Turkish

**Student:** FERİHA ÇELİK

**Supervisor: **İSMAİL NACİ CANGÜL

The main aim of this work is to find spectral (characteristic) polynomials of the eigenvalues to calculate the energy of some well-known graph types which appear in literature, to obtain relations between these graphs and recurrence relations that they satisfy, to obtain the spectrum of some graphs from the spectrum of others and to calculate the energy of these graph types. This thesis consists of four chapters. In the first chapter, definition of a graph, historical background, fundamental notions, some applications of graphs, some graph types and graph properties are recalled. These will be used throughout the thesis. In the second chapter, the spectrums are obtained for some widely-used graph types, the spectral polynomials which has the elements of the spectrum as their roots are found, and the recurrence relations to find larger spectral polynomails in terms of smaller ones are established. In the third chapter, the spectrums of the graphs C2n ve P2n+1 are obtained by means of the graphs Cn ve Pn. In the fourth chapter, some new relations which help to calculate the energy of graphs are established.