The Sum Of Distances And Mean Distance In Graph

The sum of distances in graph is just the sum of distances between all pairs of vertices of graph,this concept,introduced by the chemist wiener,it is a quite successful tool for designing quantitative structure-property relations in organic chemistry.which is closed related to another quantity-mean distance,which,denoted the average value of the distances between all pairs of vertices in graph.it is a measure of the " compactness " of a graph,it had already been initially used in architecture as atool for the evaluation of floor plans. Further more,it is used as a measure of the efficiency of a communications network.In a word this two quantitys as an important parameter of graph have been paid attention and further research by many experts.Based on the earlier times research on this two quantities.this thesis gives some researches.In chapter 2.for certain special graphs.we give some results about mean distance.In addition, we consider the relation between thesurn of distances of graph and complement graph.In chapter 3.we add edge to two kinds of special graph and discuss the sum of distances.At the mean time.we research the sum of distances or mean distance when a vertex or edge is removed from a graph.In chapter 4.we research this two quantities in a composite graph.further more ,we give the mean distance of the square of graph.In chapter 5,we discuss the mean distance in terns of other graph parameters.In the final chapter.we listed the construct of graph and some future work.