TY  - BOOK
AU  - Bıyıkoğlu,Türker
AU  - Leydold,Josef
AU  - Stadler,Peter F.
TI  - Laplacian eigenvectors of graphs: Perron-Frobenius and Faber-Krahn type theorems 
T2  - Lecture notes in mathematics,
SN  - 9783540735106
AV  - QA193 .B59 2007eb
U1  - 512.9/436 22
PY  - 2007///
CY  - Berlin, New York
PB  - Springer
KW  - Eigenvectors
KW  - Laplacian operator
KW  - Graph theory
KW  - Vecteurs
KW  - Laplacien
KW  - Teoría de grafos
KW  - embne
KW  - Laplace, Operador de
KW  - embucm
KW  - fast
N1  - Includes bibliographical references (pages 101-114) and index; Graph Laplacians -- Eigenfunctions and Nodal Domains -- Nodal Domain Theorems for Special Graph Classes -- Computational Experiments -- Faber-Krahn Type Inequalities; University staff and students only. Requires University Computer Account login off-campus
N2  - 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
UR  - https://link-springer-com.libraryproxy.ist.ac.at/10.1007/978-3-540-73510-6
ER  -