On Wiener Polarity Index And Generalize Wiener Indices Of Graphs

Observations show that:the physical and chemical properties of compounds have a closed relationship with their topological properties. Since the first topological index wiener index was introduced by Harold Wiener in1947, scientists have introduced kinds of topological indices and applied them widely to chemistry, physics and other applied disciplines. Since most of the topological indices of these chemical molecules can be transformed into the their topological structures, molecular graph, parameters, graph theory becomes naturally a powerful tool for studying the physical and chemical properties of molecules and their topological structures. As one of the most important chemical indices, wiener index and its generalizations is the research object of this paper. We focus on their calculation and the corresponding inverse structure-property problems. The main results of this work are as follows:In the second chapter, by introducing some graph transformations, we determine the min-imum Wiener polarity index of unicyclic graphs, and characterize the corresponding extremal graphs with the given diameter.In the third chapter, a lower bounds on y-Wiener index of the tensor product of graphs are obtained, as well as explicit expressions of y-Wiener index and Wiener polarity index of the tensor product of a graph and a complete multipartite graph.In the fourth chapter, we present explicit formulas of the q-Wiener index of unicyclic graphs and some composite graphs, respectively.