LEADER 03098nam 2200625 450 001 996466505103316 005 20220425091505.0 010 $a1-280-95164-8 010 $a9786610951642 010 $a3-540-73510-0 024 7 $a10.1007/978-3-540-73510-6 035 $a(CKB)1000000000437257 035 $a(EBL)3037321 035 $a(SSID)ssj0000301328 035 $a(PQKBManifestationID)11247558 035 $a(PQKBTitleCode)TC0000301328 035 $a(PQKBWorkID)10261061 035 $a(PQKB)11180946 035 $a(DE-He213)978-3-540-73510-6 035 $a(MiAaPQ)EBC3037321 035 $a(MiAaPQ)EBC6696265 035 $a(Au-PeEL)EBL6696265 035 $a(PPN)123163536 035 $a(EXLCZ)991000000000437257 100 $a20220425d2007 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aLaplacian eigenvectors of graphs $ePerron-Frobenius and Faber-Krahn type theorems /$fTu?rker B?y?kog?lu, Josef Leydold, Peter F. Stadler 205 $a1st ed. 2007. 210 1$aBerlin ;$aHeidelberg ;$aNew York :$cSpringer,$d[2007] 210 4$d©2007 215 $a1 online resource (120 p.) 225 1 $aLecture notes in mathematics (Springer-Verlag) ;$v1915 300 $a"ISSN electronic edition 1617-9692." 311 $a3-540-73509-7 320 $aIncludes bibliographical references and index. 327 $aGraph Laplacians -- Eigenfunctions and Nodal Domains -- Nodal Domain Theorems for Special Graph Classes -- Computational Experiments -- Faber-Krahn Type Inequalities. 330 $aEigenvectors of graph Laplacians have not, to date, been the subject of expository articles and thus they may seem a surprising topic for a book. The authors propose two motivations for this new LNM volume: (1) There are fascinating subtle differences between the properties of solutions of Schrödinger equations on manifolds on the one hand, and their discrete analogs on graphs. (2) "Geometric" properties of (cost) functions defined on the vertex sets of graphs are of practical interest for heuristic optimization algorithms. The observation that the cost functions of quite a few of the well-studied combinatorial optimization problems are eigenvectors of associated graph Laplacians has prompted the investigation of such eigenvectors. The volume investigates the structure of eigenvectors and looks at the number of their sign graphs ("nodal domains"), Perron components, graphs with extremal properties with respect to eigenvectors. The Rayleigh quotient and rearrangement of graphs form the main methodology. 410 0$aLecture notes in mathematics (Springer-Verlag) ;$v1915. 606 $aEigenvectors 615 0$aEigenvectors. 676 $a512.9434 700 $aB?y?kog?lu$b Tu?rker$0312250 702 $aLeydold$b Josef 702 $aStadler$b Peter F.$f1965- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466505103316 996 $aLaplacian eigenvectors of graphs$91019628 997 $aUNISA