Map Of Laplace Eigenvalues ​​of Energy And Research

After nearly half a century of rapid development, spectrum theory of graph has gradually become an important area of research in the graph theory , also it is a very active research direction. Which originated in the 18th century the graph theory have a widely range of applications in informational, cybernetics, operational research and the informations of computing science. It also closely contact with some invariant(such as diameter, chromatic number, degree sequence, connectivity, etc.) . spectrum theory of graph includes adjacency spectrum, Q-spectrum, Laplace spectrum, C-spectrum, S-spectrum, which the adjacent spectrum and Laplace Spectrum are often used. In many applications, they often require good Laplace spectral radius' lower and upper bounds.This paper studies the estimate values of the bounds of Laplace energy, as well as the upper and lower bounds of graph energy for a simple graph. Specifically includes the following aspects:Describes the some background knowledge of graph energy and the Laplace energy, and then describes the latest progress of the upper and lower bounds for the graph energy.Comparison the upper and lower bounds and its sector of the Laplace energy for some specific graphs, and then we gives some new upper and lower bounds for these graphs.Analysis the energy of graph's upper and lower bounds for different graphs , and studied the sector of the model for matrix eigenvalues of the k-th power.Analysis and comparative some of the graph which energy is greater than some specific values .