Study Of AG Index,Spectral Radius And Energy Of Graphs

The topological index of a graph is derived from the graph invariants,which can well represent the chemical bonds between chemical atoms.The energy of a graph comes from theoretical chemistry and is defined as the sum of the absolute values of all the eigenvalues of the adjacency matrix of the graph.By using graph invariants and related topological exponents,the inequality is studied and the arithmetic-geometric exponents and energy bounds of graphs are obtained.The first chapter,the research background,basic concepts and definitions of topological exponent and energy of graphs are introduced,and the research status of arithmetic-geometric index,spectral radius and energy of graphs at home and abroad are briefly introduced.The second chapter,through the analysis of related inequalities,such as Cauchy-Schwarz and Jensan’s inequality.Combining different graph invariants,the bounds of arithmetic-geometric index of graphs are obtained,and the correlated polar graphs are obtained.The third chapter,the bounds of the arithmetic-geometric spectral radius of graphs are obtained by using Rayleigh-Ritz theorem.By using spectral radius and graph invariants to analyze the inequality,the arithmetic-geometric energy bounds of general graphs and bipartite graphs are obtained,and the related polar graphs are characterized.