**Thesis Type:** Doctorate

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

**Approval Date:** 2014

**Thesis Language:** Turkish

**Student:** AYSUN YURTTAŞ

**Supervisor: **İSMAİL NACİ CANGÜL

In this work, some upper bounds for Zagreb and multiplicative Zagreb indices of graph operations are given. This thesis consits of six chapters. First chapter is introduction, and a brief summary of related literature is given in this chapter. Second chapter is preliminaries. Some basic concepts which will be used in the forthcoming chapters are introduced and some examples are given. In the third chapter, Zagreb and multiplicative Zagreb indices and coindices of graph operations are introduced and some results and theorems for Zagreb indices are given. In the fourth chapter, graph operations are introduced and some basic mathematical properties are given. In the fifth chapter, some exact expressions and theorems for the first and second Zagreb indices of graph operations including the Cartesian product, composition, join, disjunction, corona product and symmetric difference of graphs are given. The last and sixth chapter contains the original results obtained in this thesis work. In this chapter, the upper bounds on the multiplicative Zagreb indices of the join, Cartesian product, corona product, composition and disjunction of graphs are derived and the indices are evaluated for some well-known graphs.