Graph Arithmetic—spectrum And Energy Problems Of Geometric Matrices

The spectra of graph is considered as an important branch of graph theory,which is widely applied in chemistry,physical,computer science,communication network and information science technology.In the mathematical literature,graph energy is an in-variant of the spectra of graph that was formally put forward in 1978.Recently,graph energy attract the attention of a large number of mathematicians,and a large number of papers was published.This paper mainly focuses on the arithmetic-geometric matrix,and studies the arithmetic-geometric energy and spectral propertiesThe main content of this paper consists of two partsIn the first part:we give some bounds for the arithmetic-geometric spectral ra-dius and the arithmetic-geometric energy in terms of degree and some other topological indices.And find some special classes of graphs with extremal values of arithmetic-geometric energy.Finally,some families of arithmetic-geometric equienergetic graphs are constructed by graph operationsIn the second part:we compute the characteristic polynomial and energy of the arithmetic-geometric matrix of specific graphs.We also compute the characteristic poly-nomial and energy of the arithmetic-geometric matrix of specific graphs with one edge deleted.In addition,it's different from the ordinary energy that the arithmetic-geometric energy can be any integer.We also find that the arithmetic-geometric energy is greater than the Randi(?) energy for some specific graphs.