Line Graph Hyper-Wiener Index Study

Results in existed papers adequately show that the physical and chemical properties of compounds have a very closed relationship with their topological properties.Since the first topological index,Wiener index,was introduced by Harold Wiener in 1947,scholars have studied all different kinds of topological indices and applied them widely to many disciplines.Since most of the topological indices of these chemical molecules can be transformed into the their topological structures,graph theory becomes gradually a powerful tool for studying the physical and chemical properties of molecules and their topological structures.Hyper-Wiener index,as a generalization of Wiener index,one of the most important chemical indices,is the research object of this paper.This paper is about the Hyper-Wiener index of the line graph of some simple connected graphs and the main results of this work are as follows:In the first chapter,we begin to introduce the background of the Hyper-Wiener index and current research progress of related issues.Then by introducing the basic definitions,terms and icons the article involved,the paper gives the corresponding results.In the second chapter,we find the lower bound of the line graph of simple connected graphs and relationship between the original graphs and its line graphs.In the third chapter,by means of graph transformations and functional analysis,we get the upper and lower bound of the line graph of trees and unicyclic graphs and the corresponding extreme graph.