A Study Of Harary Index Of Two Kinds Of Special Tricyclic Graphs With K Pendant Points

In order to characterize the structure of molecular graphs,Plavsic and Ivanciuc independently introduce a new topological index——Harary index,which is defined as the sum of reciprocal distances of all vertex pairs in the graph.Let G(28)(V,E)be a simple connected graph with vertex set V and edge set E,respectively.If n(E)-2(28)n(V),the graph is a tricyclic graph.Classification discussion is one of the most common simple and effective reasoning methods in graph theory.Based on the tricyclic graph,this paper uses the method of classification discussion to analyze and study the Harary index of a special tricyclic graph with k pendant point,and gives the research results.The main contents of this paper are as follows:In the first chapter,first,the author introduces the research background of graph theory and the significance of the two indexes firstly.Second,it introduces the important definetion of graph theory.And then section introduces the research status of Harary index and the nearly some important research results.Finally,it introduces the main con-tents and results of this paper.In the second chapter,the author study a class of special tricyclic graphs with k pendant vertices and three circles with only one common vertex,and give a characterization of graphs with the maximal Harary index in such graphs.In the third chapter,it mainly study a class of special tricyclic graphs with k pendant vertices and three circles with a common path,and give a characterization of graphs with the maximal Harary index in such graphs.