Research On The Extremal Eccentric Distance Sum Of Graphs With Some Given Parameters

Studying the relationship between the parameters and the structures of graphs is an important research field in the modern graph theory.Let G=(VG,EG)be a simple connected graph.The eccentric distance sum(EDS)of G is defined as(?)where ?G(v)is the eccentricity of the vertex v and DG(v)=(?)dG(u,v)is the sumof all distances from the vertex v.The graph invariant was used to investigate various physical properties and deal with the date sets of analogues since it displayed high discriminating power with respect to both biological activity and physical properties.Furthermore,comparing with classical graph invariant--Wiener index,the result with regard to the study of structural activity and quantitative property by using eccentric distance sum were better.Hence,the study about the eccentric distance sum of graphs is meaningful.The concrete content of this thesis is shown as follows:In Chapter 1,we introduce the background,significance of the research and several known results.It is fully shown that our work's necessity according to the profound discussion for the research background.In Chapter 2,we offer some necessary definitions and symbols.In Chapter 3,the extemal graph that attains the minimum EDS among all k-connected graphs(resp.bipartite graphs)with given diameters are characterized.In Chapter 4,the sharp lower bound on the EDS of connected graphs of order n with given connectivity and minimum degree(resp.independence number)is determined and the corresponding extremal graph is characterized as well.In Chapter 5,we summarize the main results in this thesis and offer some prospects for further research in the future.