A Study Of Two Indices Of A Circle Containing A Given Diameter

The Wiener index is defined as the of distance over all pairs of vertices of a connected graph,and The Harary index is defined as the sum of reciprocals of distance over all pairs of vertices of a connected graph.The main contents of this article are as follows:In the first chapter,the author introduces the research background of graph theory and the significance of the two indexes firstly.Then it introduces the important definetion of graph theory and the nearly research results about two indexes.Finally,it introduces the main con-tents and results of this paper.In the second chapter,This paper gives the largest Harary index of unicycle graphs with given diameter and characterizes the extreme graphs attaining the upper bound.Specially,we also obtained the second largest extreme graphs when 4≤d≤n-3 and d(?)0(mod 2).In the third chapter,it mainly study the Wiener index of bicyclic graphs with given diam-eter and it gets the corresponding maximal Wiener index when the girth of bicyclic graphs sa-tisfies(?)＜d.