On the Laplacian spectral radius of a graph

doi:10.1016/j.laa.2003.06.007

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	On the Laplacian spectral radius of a graph
	Liu, HQ ; Lu, M ; Tian, F
	2004
发表期刊	LINEAR ALGEBRA AND ITS APPLICATIONS
ISSN	0024-3795
卷号	376 页码:135-141
摘要	Let G be a simple graph with n vertices and m edges and G(c) be its complement. Let delta(G) = delta and Delta(G) = Delta be the minimum degree and the maximum degree of vertices of G, respectively. In this paper, we present a sharp upper bound for the Laplacian spectral radius as follows: lambda(1)(G) less than or equal to (Delta + delta - 1) + root(Delta + delta - 1)(2) + 4(4m - 2delta(n-1))/2. Equality holds if and only if G is a connected regular bipartite graph. Another result Of the paper is an upper bound for the Laplacian spectral radius of the Nordhaus-Gaddum type. We prove that; lambda(1)(G) + lambda(1)(G(c)) less than or equal to n - 2 + root(Delta + delta + 1 - n)(2) + n(2) + 4(Delta - delta)(n - 1). (C) 2003 Elsevier Inc. All rights reserved.
关键词	Laplacian spectral radius minimum degree maximum degree
DOI	10.1016/j.laa.2003.06.007
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000186560300009
出版者	ELSEVIER SCIENCE INC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/19739
专题	中国科学院数学与系统科学研究院
通讯作者	Liu, HQ
作者单位	1.Tsing Hua Univ, Dept Math Sci, Beijing 100084, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Syst Sci, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Liu, HQ,Lu, M,Tian, F. On the Laplacian spectral radius of a graph[J]. LINEAR ALGEBRA AND ITS APPLICATIONS,2004,376:135-141.
APA	Liu, HQ,Lu, M,&Tian, F.(2004).On the Laplacian spectral radius of a graph.LINEAR ALGEBRA AND ITS APPLICATIONS,376,135-141.
MLA	Liu, HQ,et al."On the Laplacian spectral radius of a graph".LINEAR ALGEBRA AND ITS APPLICATIONS 376(2004):135-141.