Laplacian Eigenvectors of Graphs : Perron-Frobenius and Faber-Krahn Type Theorems
- المؤلف
- Türker Biyikoğu, Josef Leydold, Peter F. Stadler
- سنة النشر
- 2007
- الناشر
- Springer
- لغة الملف
- انكليزي
- نوع الملف
- Book
- تصنيف الكتاب
- Mathematics and Statistics
- تحميل الكتاب قراءة الكتاب
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.
الكلمات المفتاحية: Mathematics and Statistics / Eigenvector / Graph / Perron-Frobenius Theorem / Algorithms / Discrete Dirichlet problem / Graph Laplacian / Nodal domain / Vertices / Combinatorics / Matrix theory
