The Upper And Lower Bounds Of The Largest P-laplacian Eigenvalue For Graphs

Spectral graph is an important branch in graph theory.There are many researches in Laplacian eigenvalues in recent years.Recently,p-Laplacian eigenvalue was proposed and has been widely used in machine learning and computer vision fields.We improve the upper and lower bounds on the p-Laplacian eigenvalues of connected graphs proposed by Amghibech.In addition,we study the upper and lower bounds of the largestp-Laplacian eigenvalues of some special trees.The content of this article is as follows:In chapter 1,we briefly introduce research background and the state of the art in this field.In chapter 2,we improve Amghibech's results about p-Laplacian eigenvalues by using the structure properties of graphs and Jensen's inequality.In chapter 3,we study the accurate values of two special trees,namely T₁ and T₂ trees.We obtain the corresponding vectors of the p-Laplacian eigenvalues of these two kinds of trees whenis even.In chapter 4,the p-Laplacian eigenvalues of trees with e?v??2,paths and T_? trees are studied.For trees of e?v??2,the upper bound of trees with e?v??2 is obtained by using the properties of concave functions based on the work of Amghibech.For the paths and T_? trees,based on the work of Dragan Stevanovic,we use Holder inequality and the basic properties of the graph to get the upper and lower bounds of the largest p-laplacian eigenvalue of paths and T_? trees.