---

＜電子ブック＞
Laplacian Eigenvectors of Graphs : Perron-Frobenius and Faber-Krahn Type Theorems / by Türker Biyikoglu, Josef Leydold, Peter F. Stadler
(Lecture Notes in Mathematics. ISSN:16179692 ; 1915)

版	1st ed. 2007.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2007
本文言語	英語
大きさ	VIII, 120 p : online resource
著者標目	*Biyikoglu, Türker author Leydold, Josef author Stadler, Peter F author SpringerLink (Online service)
件　名	LCSH:Algebra LCSH:Discrete mathematics LCSH:Algebras, Linear FREE:Algebra FREE:Discrete Mathematics FREE:Linear Algebra
一般注記	Graph Laplacians -- Eigenfunctions and Nodal Domains -- Nodal Domain Theorems for Special Graph Classes -- Computational Experiments -- Faber-Krahn Type Inequalities 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 HTTP:URL=https://doi.org/10.1007/978-3-540-73510-6

 類似資料