图的Laplacian矩阵和拟-Laplacian矩阵的谱半径

摘要

1) Some new upper bounds of spectral radius of Laplacian matrices of graphs are obtained, these bounds are tight and better than those bygone days. 2) Some tight bounds of spectral radius of quasi-Laplacian matrices of graphs are given, which will play an important role in studying the spectrum of quasi-Laplacian matrices of graphs.%1)给出了图的Laplacian矩阵谱半径的一些新的上界,这些界是紧的且比已有的结果都好.2)给出了图的拟-Laplacian矩阵谱半径的一些紧的界,这些界对进一步研究图的拟-Laplacian矩阵的谱将起到重要的作用.