Research On Matching Energy Of Complete Multipartite Graphs And Some Sparse Graphs

In 2012,Gutman and Wagner proposed the concept of the matching energy of graphs.Let G be a simple graph of order n.The matching energy of G,denoted by ME(G),is defined as(?),where m(G,k)is the number of k-matchings of G.In this thesis,we study the matching energies of complete multipartite graphs and some sparse graphs and characterize the extremal graphs attaining the minimum matching energy among these graphs.In Chapter 1,we introduce the background knowledge of the studied problems and the academic status,and then present a summary of the main results of this thesis.In Chapter 2,we study the matching energy of m-multipartite complete graphs and characterize the extremal graphs attaining the minimum matching energy among these graphs.Moreover,we also obtain related results for the Hosoya index of m-multipartite complete graphs.In Chapter 3,we study the unicyclic graphs,with fixed number of pendant vertices and the unique cycle contains exactly one vertex having degree more than 2,and charac-terize the extremal graphs attaining the minimum matching energy among these graphs.Moreover,we also obtain related results for the Hosoya index of these graphs.In Chapter 4,we study the unicyclic graphs,the bicyclic graphs and the book graphs with given partition conditions and characterize the extremal graphs attaining the min-imum matching energy among them.Moreover,we also obtain related results for the Hosoya index of these three classes of graphs.