Research On Extremal Problems Of The Mostar Indices Of Unicyclic Graphs And Bicyclic Graphs With A Given Diameter

Do(?)li(?) et al.introduced a distance-based topological index,namely Mostar index in 2018.Given a connected G,the Mostar index Mo(G)is defined as whereun is the number of vertices of G closer to vertex u than to vertex v,andvn is the the number of vertices of G closer to vertex v than to vertex u.In this dissertation,we study the maximum Mostar index of all the n-vertex unicyclic graphs and bicyclic graphs with a given diameter d,and characterize the corresponding extremal graphs.The main contents include:· In Chapter 1,we introduce the research background and significance of this paper,as well as the research results and progress of Mostar index at home and abroad.And we give the main results obtained in the dissertation.· In Chapter 2,we introduce the basic concepts and notations involved in this dissertation,and gives some necessary lemmas.· In Chapter 3,the upper bounds on the Mostar index and the extremal graphs in the class of all n-vertex unicyclic graphs with a given diameter d are characterized.· In Chapter 4,the maximum Mostar index of all n-vertex unicyclic graphs with a given diameter d satisfying the condition of 8 ≤d ≤n-7 is determi-ned,and find the corresponding extremal graphs.· In Chapter 5,we summarize the main results in this dissertation and put forward several directions for further research.