Laplacian eigenvectors of graphs : Perron-Frobenius and Faber-Krahn type theorems
著者
書誌事項
Laplacian eigenvectors of graphs : Perron-Frobenius and Faber-Krahn type theorems
（Lecture notes in mathematics, 1915）
Springer, c2007
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注記
Includes bibliographical references (p. [101]-111) and index
内容説明・目次
内容説明
This fascinating volume investigates the structure of eigenvectors and looks at the number of their sign graphs ("nodal domains"), Perron components, and graphs with extremal properties with respect to eigenvectors. The Rayleigh quotient and rearrangement of graphs form the main methodology. Eigenvectors of graph Laplacians may seem a surprising topic for a book, but the authors show that there are subtle differences between the properties of solutions of Schroedinger equations on manifolds on the one hand, and their discrete analogs on graphs.
目次
Graph Laplacians.- Eigenfunctions and Nodal Domains.- Nodal Domain Theorems for Special Graph Classes.- Computational Experiments.- Faber-Krahn Type Inequalities.
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