Topological Index Of Several Classes Of Graphs

Topological index is an important research topic in chemical graph theory.It is a way of numeralization of molecular structure.It can be used to describe chemical structure and a graph invariant reflecting the structural characteristics of compounds.Randi?index,GA index,harmonic index,general sum-connectivity index in this paper are all topological indices based on the degree of vertices.In this paper,the four topological indices are studied in tetracyclic graphs,tricyclic graphs,cacti,corona graphs and alkanes graphs respectively.In chapter 1,introduces the research background,significance and current situation of topological index,gives some basic concepts,relevant conclusions and the main research results of this paper.In chapter 2,by using the relation of vertex degree and taking the exponential value of a special quadruple graph as a bound,it is proved that the Randi?index of most tetracyclic graphs are less than this bound value.Finally,the first nine Randi?index and their corresponding graph structures are given.The method is simpler and more generalizable.In chapter 3,it is proved that the GA index of most tricyclic graphs are less than bounds,and then the first six GA index and corresponding polar graphs are given.In chapter 4,according to mathematical induction,the minimal harmonic index of cactus graph is obtained.In chapter 5,according to the definition of corona graphs,we obtained the structure ofP_n?P_m,P_n?P_m,C_n?C_m,P_n?C_mandC_n?P_m,and the specific values of GA index and harmonic index.In chapter 6,according to the definition of alkane class graphs,CnH2n+2 alkane class graphs,U_n~p uncyclic graphs,CnH2n naphthene class graphs,CnH2n+1alkyl or alkyl branched chain class graphs,putting alkyl or alkyl branched chain in hydrogen atom space of naphthene,the general sum-connectivity index,GA index and harmonic index of new chemical class diagram are obtained.