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Laplacian Eigenvectors of Graphs : Perron-Frobenius and Faber-Krahn Type Theorems
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 Schröding...
| Auteurs principaux : | , , |
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| Format : | Livre |
| Langue : | anglais |
| Titre complet : | Laplacian Eigenvectors of Graphs : Perron-Frobenius and Faber-Krahn Type Theorems / Türker Biyikoglu, Josef Leydold, Peter F. Stadler. |
| Édition : | 1st ed. 2007. |
| Publié : |
Berlin, Heidelberg :
Springer Berlin Heidelberg
, [20..] Cham : Springer Nature |
| Collection : | Lecture notes in mathematics (Internet) ; 1915 |
| Accès en ligne : |
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| Condition d'utilisation et de reproduction : | Conditions particulières de réutilisation pour les bénéficiaires des licences nationales : https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 |
| Contenu : | Graph Laplacians. Eigenfunctions and Nodal Domains. Nodal Domain Theorems for Special Graph Classes. Computational Experiments. Faber-Krahn Type Inequalities |
| Sujets : | |
| Documents associés : | Autre format:
Laplacian eigenvectors of graphs Autre format: Laplacian Eigenvectors of Graphs Autre format: Laplacian eigenvectors of graphs |
| Résumé : | 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 |
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| Notes : | L'impression du document génère 120 p. |
| Bibliographie : | Bibliogr. Index |
| ISBN : | 978-3-540-73510-6 |
| DOI : | 10.1007/978-3-540-73510-6 |