On Spectra Of Edge-covering Of Graphs

Algebraic graph theory is a branch of graphtheory that utilizes the al-gebraic properties of the associated matrices of a graph to study a graph.While the spectral graph theory is an important branch of algebraic graph theory,it investigates the spectra of the associated matrices of a graph and the relations between the spectra and properties of a graph.The study on spectral graph theory has been very active for many years.Many mature and important achievements and applications have also been obtained.A very important part of spectral graph theory is to study the computing the ad-jacency spectrum,normalized laplacian spectrum and laplacian spectrum of 2-edge-covering graphs and 3-edge-covering graphs.This thesis includes three chapters.The first chapter is an introduction,in which the basic concepts,knowledge of spectral graph theory and the main issues discussed later are briefly introduced.Second chapter mainly studies relationship between 2-edge-covering and laplacian spectrum,obtained the graph laplacian spectrum is it 2-edge-covering of a modified hybrid graph and the cover of the graph laplacian spectrum and repeatedly.Third chapter mainly studies 3-edge-covering and spectrum,the relation-ship between the adjacency spectrum,normalized laplacian spectrum,laplacian spectrum 3-edge-covering of the spectrum is that it overlays the graph of a modified weighted and edge points are mixed weighted graph.