The General Vertex-PI Index And Nordhaus-Gaddum-type Inequality For Some Topological Indices

This thesis is divided into four chapters. Chapter 1 consists of two sections. In sec-tion 1, we introduce briefly the history of some topological indices of graphs. In section 2, we will present some well-known results. Chapter 2 consists of two sections. In section 1, we mainly introduce the general vertex-PI index of Cartesian product graphs. In section 2, we show some results about join graphs. Chapter 3 consists of two sections. In section 1, we mainly introduce the Nordhaus-Gaddum-type-I inequalities for some graphs. In section 2, we show the Nordhaus-Gaddum-type-II inequalities for some graphs.