Limits and different approaches to arithmetic-geometric index

The thesis includes studies on the Arithmetic-Geometric index defined by graph degrees. Arithmetic-Geometric index has been examined in three different ways. Firstly, relationships between the vertex degrees of the graph and different indices are established and bounded for the Arithmetic-Geometric index. Secondly, Arithmetic-Geometric index was defined for positive weighted graphs and positive interval weighted graphs and graph operations were performed. Thirdly, the Arithmetic-Geometric index was explained in the geometric plane and different indices were obtained. It was calculated values of these indexes for special graphs.