The K-Szeged Index Of Graphs

Compounds molecular structure determines the chemical and physical properties,the physiological activity,pharmacological activity and the physicalchemical properties of compounds can be obtained by study the topological index of molecular graphs.The study of the molecular topological index has been widely applied in communication network,information science,physics and chemistry,etc.Based on the Szeged index of graphs and the Steiner Wiener index of trees,we proposed a novel concept in this paper,i.e.,k-Szeged index,and similar to the revised Szeged index,we also introduce the revised k-Szeged index.In this thesis,we mainly study the upper and lower bounds and the Nordhaus-Gaddum-type results of the(revised)k-Szeged indices of connected graphs,the extremal values and extremal graph of(revised)k-Szeged indices of complete bipartite graphs,unicyclic graphs with order n,and hexagonal chains with ? hexagons.Here is the main work in this paper:In chapter 2,by combinatorial inequalities,we determine the upper and lower bounds of the(revised)k-Szeged indices for a connected graph with order nand size m,the Nordhaus-Gaddum-type results of(revised)k-Szeged indices of connected graphs with order n,the extremal values and extremal graph of(revised)k-Szeged indices of complete bipartite.In chapter 3,by the properties of the Steiner Wiener index of trees,combinatorial inequality,the monotonicity of the function,firstly,we determine the extremal values and extremal graph of(revised)k-Szeged indices of unicyclic with even girth.Then,we determine the extremal values and extremal graph of revised k-Szeged index of unicyclic with odd girth.In chapter 4,by graphs transformation,we determine the extremal values and corresponding extremal graph of(revised)k-Szeged indices of hexagonal chains.