Remarks on Spectral Radius and Laplacian Eigenvalues of a Graph期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

Remarks on Spectral Radius and Laplacian Eigenvalues of a Graph

Authors:

Institution:

(1) Department of Mathematics, South China Normal University, Guangzhou, 510631, P. R. China;(2) Department of Mathematics Education, Seoul National University, Seoul, 151-742, Korea

Abstract:

Let G be a graph with n vertices, m edges and a vertex degree sequence (d ₁, d ₂,..., d _n), where d ₁ ≥ d ₂ ≥ ... ≥ d _n. The spectral radius and the largest Laplacian eigenvalue are denoted by ϱ(G) and μ(G), respectively. We determine the graphs with

$\varrho (G) = \frac{{d_n - 1}}{2} + \sqrt {2m - nd_n + \frac{{(d_n + 1)^2 }}{4}}$

and the graphs with d _n ≥ 1 and

$\mu (G) = d_n + \frac{1}{2} + \sqrt {\sum\limits_{i - 1}^n {di(di - dn) + } \left( {d_n - \frac{1}{2}} \right)^2 .}$

We also present some sharp lower bounds for the Laplacian eigenvalues of a connected graph. The work was supported by National Nature Science Foundation of China (10201009), Guangdong Provincial Natural Science Foundation of China (021072) and Com²MaC-KOSEF

Keywords:

spectral radius Laplacian eigenvalue strongly regular graph

本文献已被 SpringerLink 等数据库收录！

设为首页 | 免责声明 | 关于勤云 | 加入收藏