On the Sum of Laplacian Eigenvalues of Graphs

Let k be a natural number and let G be a graph with at least k vertices. A.E. Brouwer conjectured that the sum of the k largest Laplacian eigenvalues of G is at most e(G) (k choose 2), where e(G) is the number of edges of G. We prove this conjecture for k = 2. We also show that if G is a tree, then the sum of the k largest Laplacian eigenvalues of G is at most e(G) 2k-1

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Year of publication:	[2008]
Authors:	Haemers, Willem H.
Other Persons:	Mohammadian, Ali (contributor) ; Tayfeh-Rezaie, Behruz (contributor)
Publisher:	[2008]: [S.l.] : SSRN
Subject:	Graphentheorie \| Graph theory \| Mathematik \| Mathematics \| Deskriptive Statistik \| Descriptive statistics

Extent:	1 Online-Ressource (10 p)
Series:	CentER Discussion Paper Series ; No. 2008-98
Type of publication:	Book / Working Paper
Language:	English
Notes:	Nach Informationen von SSRN wurde die ursprüngliche Fassung des Dokuments November 18, 2008 erstellt
Other identifiers:	10.2139/ssrn.1313701 [DOI]
Classification:	C0 - Mathematical and Quantitative Methods. General
Source:	ECONIS - Online Catalogue of the ZBW

Persistent link: https://www.econbiz.de/10012722415