On The Extremal Matching Energy In Several Classes Of Graphs

In 2012, Gutman and Wagner first introduced the notion of matching energy of graphs closely related to graph energy and developed the fundamental theory in this field. Since then, matching energy has attracted much attention, especially to the extremal matching energy for some graphs. Base on the work founded in the field and by the matching theory, this paper has studied the extremal matching energy of two sets of graphs.In Chapter 1, we briefly present the development background of graph theory、the energy and matching energy. And some basic definitions and standard notations in the theory of matching energy are listed there as well.In Chapter 2, applying cases discussion and mathematical induction, we characterize the graph with minimal matching energy, among all unicyclic graphs except Qnl,k on n vertices with girth l and k pendent vertices, that is, Rnl,k has the minimal matching energy. And we compare the matching energy of Qnl,k with that of Rnl,k in some degree.In Chapter 3, among the set of unicyclic graphs with given order and maximum degree, we characterize the graphs with maximum matching energy in two cases according to whether there exists a maximum degree vertex on the unique cycle or not, where the relationship between the order and maximum degree is also taken into account.In last chapter, a summary on the thesis is given and some further development on the topic is predicted.