The Szeged Index Of Graphs

Ibpological indices are widely used in theoretical chemistry to establish the relations between the structure and the properties of molecules. They provide correlations with physical chemical and thermodynamic parameters of chemical compounds. The Wiener index and Szeged index are two important topological indices in theoretical chemistry.The Szeged index coincides with the Wiener index on trees. Recently, the Szeged index has received much attention for its mathematical properties and chemical applications. The research on Szeged index mainly focus on two direction: the first is studying the bounds of Szeged index, and the second is studying the graphs with maximum or minimum Szeged index in some class of graphs. In this paper, we mainly characterize the graph with minimum Szeged index in unicyclic graph with given diameter.The thesis is divided into four chapters. In Chapter 1, we introduce research background of Szeged index, and some notations of graphs. In Chapter 2, we summarize research development of Wiener index, Szeged index and revised Szeged index of graphs, respectively. In Chapter 3, we mainly present the proof of main result. Finally, a summary is given and some problems to be further studied are discussed.