Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 0795.05092
Grone, Robert; Merris, Russell
The Laplacian spectrum of a graph. II. (English)
[J] SIAM J. Discrete Math. 7, No.2, 221-229 (1994). ISSN 0895-4801; ISSN 1095-7146/e

Summary: [For Part I see {\it R. Grone}, {\it R. Merris} and {\it V. S. Sunder}, SIAM J. Matrix Anal. Appl. 11, No. 2, 218-238 (1990; Zbl 0733.05060).]\par Let $G$ be a graph. Denote by $D(G)$ the diagonal matrix of its vertex degrees and by $A(G)$ its adjacency matrix. Then $L(G) = D(G) -A(G)$ is the Laplacian matrix of $G$. The first section of this paper is devoted to properties of Laplacian integral graphs, those for which the Laplacian spectrum consists entirely of integers. The second section relates the degree sequence and the Laplacian spectrum through majorization. The third section introduces the notion of a $d$-cluster, using it to bound the multiplicity of $d$ in the spectrum of $L(G)$.

MSC 2000:: *05C50 Graphs and matrices

Keywords: diagonal matrix; adjacency matrix; Laplacian matrix; Laplacian integral graphs; Laplacian spectrum; degree sequence; majorization

Citations: Zbl 0733.05060

Cited in: Zbl 1227.05181 Zbl 1192.05090

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Simple Search

Zentralblatt MATH Berlin [Germany]