Laplacian eigenvectors of graphs : Perron-Frobenius and Faber-Krahn type theorems / Türker Bıyıkoğlu, Josef Leydold, Peter F. Stadler.

By:

Bıyıkoğlu, Türker

Contributor(s):

Material type: Text

text

Media type:

computer

Carrier type:

online resource

ISBN:

9783540735106
3540735100
3540735097
9783540735090

Subject(s):

Additional physical formats: Print version:: Laplacian eigenvectors of graphs.DDC classification:

512.9/436 22

LOC classification:

QA193 .B59 2007eb

Online resources:

Click here to access online

Contents:

Graph Laplacians -- Eigenfunctions and Nodal Domains -- Nodal Domain Theorems for Special Graph Classes -- Computational Experiments -- Faber-Krahn Type Inequalities.

Summary: Eigenvectors of graph Laplacians have not, to date, been the subject of expository articles and thus they may seem a surprising topic for a book. The authors propose two motivations for this new LNM volume: (1) There are fascinating subtle differences between the properties of solutions of Schrödinger equations on manifolds on the one hand, and their discrete analogs on graphs. (2) "Geometric" properties of (cost) functions defined on the vertex sets of graphs are of practical interest for heuristic optimization algorithms. The observation that the cost functions of quite a few of the well-studied combinatorial optimization problems are eigenvectors of associated graph Laplacians has prompted the investigation of such eigenvectors. The volume investigates the structure of eigenvectors and looks at the number of their sign graphs ("nodal domains"), Perron components, graphs with extremal properties with respect to eigenvectors. The Rayleigh quotient and rearrangement of graphs form the main methodology

Holdings ( 1 )
Title notes ( 5 )

Holdings
Item type	Current library	Collection	Call number	Status	Date due	Barcode	Item holds
eBook	e-Library	eBook LN Mathematic		Available

Total holds: 0

Includes bibliographical references (pages 101-114) and index.

Print version record.

Graph Laplacians -- Eigenfunctions and Nodal Domains -- Nodal Domain Theorems for Special Graph Classes -- Computational Experiments -- Faber-Krahn Type Inequalities.

Eigenvectors of graph Laplacians have not, to date, been the subject of expository articles and thus they may seem a surprising topic for a book. The authors propose two motivations for this new LNM volume: (1) There are fascinating subtle differences between the properties of solutions of Schrödinger equations on manifolds on the one hand, and their discrete analogs on graphs. (2) "Geometric" properties of (cost) functions defined on the vertex sets of graphs are of practical interest for heuristic optimization algorithms. The observation that the cost functions of quite a few of the well-studied combinatorial optimization problems are eigenvectors of associated graph Laplacians has prompted the investigation of such eigenvectors. The volume investigates the structure of eigenvectors and looks at the number of their sign graphs ("nodal domains"), Perron components, graphs with extremal properties with respect to eigenvectors. The Rayleigh quotient and rearrangement of graphs form the main methodology

University staff and students only. Requires University Computer Account login off-campus.