Prime ideal sum graph and commuting graph of gamma rings

Concepts from the two main disciplines of mathematics, algebra and discrete mathematics, are extended from one to the other to build bridges between these two fields. Graphs constructed from algebraic structures have been studied by many mathematicians and have become an important area of research. Associating rings with graphs plays a critical role in studying the structure of rings. The study of these graphs leads to some conclusions about algebraic structures. On the other hand, the properties of the algebraic structure provide information about the graphs derived from this structure. In this study, we define commuting graphs and prime ideal sum graphs on gamma rings. As a result, the information that the properties of the gamma ring can give about the defined graph is investigated. Similarly, it is analyzed what the properties of the defined graph can tell us about the structure of the gamma ring. In accordance with this purpose, in the first part of the thesis, some of the papers on graphs defined by using the ring were summarized and in the following chapters of the thesis, it was decided to consider the prime ideal sum graph and commuting graph for gamma rings.