The Maximum Problem Of Two Topological Indices Of Tetracyclic Graphs

The molecular topological index of a graph is a way to numerical graph invariants applicable in chemistry.It plays an important role in mathematical chemistry,especially in the study of QSPR/QSAR.In this paper,we study the maximum problem of harmonic indices and GA indices of tetracyclic graphs,and we characterized the corresponding structure of extremal graphs.In chapter 1,we introduced the background of the molecular topological index of a graph,and the relevant definitions of graph theory.We introduced the history and the development of harmonic index and GA index of graphs.In chapter 2,according to the edge structure of graphs,we defined eleven kinds of tetracyclic graphs.We study the harmonic indices of n-vertices tetracyclic graphs.And we determined the first up to eighth maximum harmonic indices of n-vertices tetracyclic graphs when n?9 through classified discussion,and characterized the corresponding structure of extremal graphs.In chapter 3,we study the harmonic indices of n-vertices tetracyclic graphs.And we determined the first up to fourth maximum GA indices of n-vertices tetracyclic graphs when n?9 through classified discussion,and characterized the corresponding structure of extremal graphs.