Research On Wiener Index Of Graphs

The Wiener index of a graph is just the sum of distance between all unordered pairs of vertices of the graph.This concept,introduce by the chemist Wiener,is a quite successful tool for designing quantitative structure property relations in organic chemistry,which is closed related to another concept-mean distance,which denoted the average value of the the distance between all unordered pairs of vertices in graph.In a word,Graph-Theory can be used to discribe the structure of molecule,as an useful math mathmatical lanuage. So it is a good tool that is for the wiener index.we will use the standard language of graph theory and study this important index.In chapter 1:We introduce some important topological index and basic terminology and notations,we give a brief overview to the main results of thesis.In chapter 2:We discribe the ordering trees by their wiener indices in T_n⁴.We obtain some the ordering of the trees in T_n⁴ by their wiener indices.Based on the relations,Meanwhile we get the trees in T∈T_{l11,p11,p12,p13,l12}¹ with the first down to 7th biggest wiener indices.In chapter 3:We can add up one or two edages to the trees with only has one two nopedent edages,then we received the ordering of theirs.In chapter 4:We characterize all trees with thirdest largest,forth largest,fifth largest,and sixth largest value of their wiener indexIn chapter 5:We propse some problems for farther reasure wiener index...