On the Distribution of Laplacian Eigenvalues of a Graph  

作　　者：Ji Ming GUO Xiao Li WU Jiong Ming ZHANG Kun Fu FANG 

机构地区：[1]Department of Applied Mathematics, China University of Petroleum, Dongying 257061, P. R. China [2]Faculty of Science, Huzhou Teachers College, Huzhou 313000, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2011年第11期2259-2268,共10页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China （Grant No. 10871204） and the Fundamental Research Funds for the Central Universities （Grant No. 09CX04003A）

摘　　要：This paper presents some bounds on the number of Laplacian eigenvalues contained in various subintervals of [0, n] by using the matching number and edge covering number for G, and asserts that for a connected graph the Laplacian eigenvalue 1 appears with certain multiplicity. Furthermore, as an application of our result （Theorem 13）, Grone and Merris＇ conjecture [The Laplacian spectrum of graph II. SIAM J. Discrete Math., 7, 221-229 （1994）] is partially proved.This paper presents some bounds on the number of Laplacian eigenvalues contained in various subintervals of [0, n] by using the matching number and edge covering number for G, and asserts that for a connected graph the Laplacian eigenvalue 1 appears with certain multiplicity. Furthermore, as an application of our result （Theorem 13）, Grone and Merris＇ conjecture [The Laplacian spectrum of graph II. SIAM J. Discrete Math., 7, 221-229 （1994）] is partially proved.

关 键 词：Laplacian eigenvalue matching number edge covering number PENDANT NEIGHBOR 

分 类 号：O151.21[理学—数学] TP391.41[理学—基础数学]