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Cover: 9783540735090 | Laplacian Eigenvectors of Graphs | Türker Biyikoglu (u. a.) | Buch
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Laplacian Eigenvectors of Graphs
Perron-Frobenius and Faber-Krahn Type Theorems
Taschenbuch von Türker Biyikoglu (u. a.)
Sprache: Englisch

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Lieferzeit 4-7 Werktage

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Beschreibung
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.

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.

Inhaltsverzeichnis
Graph Laplacians.- Eigenfunctions and Nodal Domains.- Nodal Domain Theorems for Special Graph Classes.- Computational Experiments.- Faber-Krahn Type Inequalities.
Details
Erscheinungsjahr: 2007
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 120
Inhalt: viii
120 S.
ISBN-13: 9783540735090
ISBN-10: 3540735097
Sprache: Englisch
Herstellernummer: 978-3-540-73509-0
Autor: Biyikoglu, Türker
Leydold, Josef
Stadler, Peter F.
Hersteller: Springer
Springer, Berlin
Springer Berlin Heidelberg
Abbildungen: VIII, 120 p.
Maße: 8 x 157 x 236 mm
Von/Mit: Türker Biyikoglu (u. a.)
Erscheinungsdatum: 26.07.2007
Gewicht: 0,209 kg
preigu-id: 101997844
Inhaltsverzeichnis
Graph Laplacians.- Eigenfunctions and Nodal Domains.- Nodal Domain Theorems for Special Graph Classes.- Computational Experiments.- Faber-Krahn Type Inequalities.
Details
Erscheinungsjahr: 2007
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 120
Inhalt: viii
120 S.
ISBN-13: 9783540735090
ISBN-10: 3540735097
Sprache: Englisch
Herstellernummer: 978-3-540-73509-0
Autor: Biyikoglu, Türker
Leydold, Josef
Stadler, Peter F.
Hersteller: Springer
Springer, Berlin
Springer Berlin Heidelberg
Abbildungen: VIII, 120 p.
Maße: 8 x 157 x 236 mm
Von/Mit: Türker Biyikoglu (u. a.)
Erscheinungsdatum: 26.07.2007
Gewicht: 0,209 kg
preigu-id: 101997844
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