Bounds On The AG Spectral Radius And AG Energy Of Graphs

Graph energy is a very important research topic in graph theory,which has a wide range of research prospects and has become a hot research topic in recent years.In chemical graph theory,the definition of graph energy comes from the approximate estimation of molecular orbital of all ?-electron energy.In this paper,we mainly study the bounds on the arithmetical-geometric spectral radius and energy of graphs.The first chapter introduces the research background of graph energy,the definition of basic concepts in graph theory,and the research status of arithmetic-geometric spectral radius and energy of graphs at home and abroad,and briefly expounds the main conclusions of this paper.The second chapter,we use some lemmas,such as Perron Frobenius theorem,to calculate the bounds of arithmetic-geometric spectral radius.In this paper,we use some invariants of graph,such as vertex number,edge number,maximum degree,minimum degree,etc.to depict the bounds of arithmetic-geometric spectral radius of graph,and characterize the extremal graphs.The third chapter,through Ozeki's inequality,Polya-Szeg(?) inequality,H(?)lder inequality and other related lemma,the arithmetic-geometric energy of the graph is appropriately scaled down,and some invariants of the graph,such as the number of vertices,the number of edges,the maximum degree,the minimum degree,and the topological index of the graph,are used to describe the bounds of the arithmetic-geometric energy of the graphs,and characterize the extremal graphs.