03098nam 2200625 450 99646650510331620220425091505.01-280-95164-897866109516423-540-73510-010.1007/978-3-540-73510-6(CKB)1000000000437257(EBL)3037321(SSID)ssj0000301328(PQKBManifestationID)11247558(PQKBTitleCode)TC0000301328(PQKBWorkID)10261061(PQKB)11180946(DE-He213)978-3-540-73510-6(MiAaPQ)EBC3037321(MiAaPQ)EBC6696265(Au-PeEL)EBL6696265(PPN)123163536(EXLCZ)99100000000043725720220425d2007 uy 0engur|n|---|||||txtccrLaplacian eigenvectors of graphs Perron-Frobenius and Faber-Krahn type theorems /Türker Bıyıkoğlu, Josef Leydold, Peter F. Stadler1st ed. 2007.Berlin ;Heidelberg ;New York :Springer,[2007]©20071 online resource (120 p.)Lecture notes in mathematics (Springer-Verlag) ;1915"ISSN electronic edition 1617-9692."3-540-73509-7 Includes bibliographical references and index.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.Lecture notes in mathematics (Springer-Verlag) ;1915.EigenvectorsEigenvectors.512.9434Bıyıkoğlu Türker312250Leydold JosefStadler Peter F.1965-MiAaPQMiAaPQMiAaPQBOOK996466505103316Laplacian eigenvectors of graphs1019628UNISA