| Topological index is an important research field in chemical graph theory.It is called the index based on vertex degree,according to the topological index defined by the degree of adjacent vertices in a graph.In the research of topological index,the research based on degree index is particularly extensive.In order to study the index based on degree effectively,using the idea of binary function f(x,y),the connection function R_f is defined systematically.In this paper,we study the extremal problem of degree based exponential function of bicyclic graph and tricyclic graph with given degree sequence.The first chapter introduces the research background,significance and the development of connection function.Secondly,the related basic concepts and the research status of connection function are introduced.Finally,the main conclusions of this paper are expounded.In second chapter,in order to obtain the maximize or minimize R_f for a given degree sequence of bicyclic graphs,the extremal graphs on the bicyclic graphs are obtained using proof by contradiction,and an algorithm is given to construct the extremal graph.In Chapter 3,we classified tricyclic graphs into four classes according to the size of root points of a given degree sequence,discussed four kinds of tricyclic graphs respectively,and obtained the maximize or minimize R_f for a given degree sequence of tricyclic graphs. |
