The Spectral Radius And Energy Of Arithmetic-geometric Adjacency Matrix Of Graph

The energy of the graph is the sum of the absolute values of the eigenvalues of the graph adjacency matrix.In recent years,according to different chemical indices and other research needs,the research of empowerment graph energy has become one of the hot issues of many scholars.By means of the energy problem corresponding to the topological index of degree-based graph,the arithmetic-geometric energy problem of some special graphs is studied by using the analytical theory and the scaling of basic inequalities.The bounds of the Arithmetic-geometry Estrada index of graph and the spectral radius and energy of a class of weighted graphs are studied accordingly.This article is divided into four chapters as follows:In chapter 1,it is the clue.In chapter 2,we use the ordinary energy,the maximum degree,the minimum degree problem and the modified second Zagreb index and the order of the graph to obtain two upper bounds of the Arithmetic-geometric energy of the graph.And the relationship between the Arithmetic-geometric energy and the ordinary energy is found.In addition we get some upper bounds of Arithmetic-geometric energy of tree,double circle and single circle using the techniques of analysis and inequality and the relationship between Arithmetic-geometric energy and ordinary energy;In chapter 3,according to the number of vertices,the number of edges and characterize the extremal graphs,some upper and lower bounds of Arithmetic-geometric Estrada energy of simple graph are obtained,and the bounds of bipartite graph are given;In chapter 4,on the basis of the ISI index,let the edge weight of the graph G is di+dj/didj,and then the spectral radius and energy of graph are studied.According to the Nordhaus-Gaddum-Type relation,we obtain some upper and lower bounds of the spectral radius and energy of the weighted graph.