On Topological Indices Of Some Graphs With Given Matching Number

The physical and chemical properties of a compound(such as boiling point,melting point,biological activity,etc.)are determined by the molecular structure of the compound.The topological index of molecular graph of a compound is closely related to its chemical structure,so the molecular structure information of a compound can be explored by studying the topological index of molecular graph of a compound,so as to predict the physical and chemical properties,pharmacological activity,and physiological activity of the compound.The topological index of graphs is an important branch of graph theory and applied research.This article mainly studies the extremal value problems of topological indices of some graphs with given matching number.The full text is divided into five chapters,as follows:In Chapter 1,we introduce some elementary concept of graph theory,symbols,definitions of several indices and current research progress at home and abroad.In Chapter 2,using edge lifting transformation,branch transformation and contraction cycle transformation,we give the extremal values and extremal graph of Szeged index among trees and unicyclic graphs with perfect matchings.In Chapter 3,we study the extremal values of hyper-Zagreb index of some graphs.We first consider the extremal values of hyper-Zagreb index among cacti with perfect matchings.Afterwards,we study the extremal values of hyper-Zagreb index among unicyclic graphs and bicyclic graphs with given matching number.At last,we give the extremal values of hyper-Zagreb index among bipartite graphs with given matching number.In Chapter 4,we study the extremal values of edge Mostar index of some graphs.We first consider the extremal values of edge Mostar index among trees and unicyclic graphs.Afterwards,we determine the maximum value of edge Mostar index among cacti,and characterize the corresponding extremal graphs.At last,we determine the second maximum value of edge Mostar index among cacti,and characterize the corresponding extremal graphs.In Chapter 5,we summarize the main work of this thesis and raise some prospects for future work.