Sharp Upper Bounds for the Laplacian Spectral Radius of Graphs-Reference-Cited by-同舟云学术

Sharp Upper Bounds for the Laplacian Spectral Radius of Graphs

Published:2013 Issue: Volume:2013 Page:1-4
ISSN:1024-123X
Container-title:Mathematical Problems in Engineering
language:en
Short-container-title:Mathematical Problems in Engineering

Author:

Zhou Houqing¹^ORCID,Xu Youzhuan²

Affiliation:

1. Department of Mathematics, Shaoyang University, Hunan 422000, China

2. Shaoyang Radio & TV University, Hunan 422000, China

Abstract

The spectrum of the Laplacian matrix of a network plays a key role in a wide range of dynamical problems associated with the network, from transient stability analysis of power network to distributed control of formations. LetG=(V,E)be a simple connected graph onnvertices and letμ(G)be the largest Laplacian eigenvalue (i.e., the spectral radius) ofG. In this paper, by using the Cauchy-Schwarz inequality, we show that the upper bounds for the Laplacian spectral radius ofG.

Funder

Hunan Provincial Natural Science Foundation

Publisher

Hindawi Limited

Subject

General Engineering,General Mathematics

Link

http://downloads.hindawi.com/journals/mpe/2013/720854.pdf

Reference10 articles.

1. Master Stability Functions for Synchronized Coupled Systems

2. Synchronization and Transient Stability in Power Networks and Nonuniform Kuramoto Oscillators

3. Consensus and Cooperation in Networked Multi-Agent Systems

4. Laplacian matrices of graphs: a survey

5. Bounds on the (Laplacian) spectral radius of graphs

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