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001 978-3-540-73510-6
003 DE-He213
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007 cr nn 008mamaa
008 100301s2007 gw | s |||| 0|eng d
020 _a9783540735106
_9978-3-540-73510-6
024 7 _a10.1007/978-3-540-73510-6
_2doi
050 4 _aQA150-272
072 7 _aPBF
_2bicssc
072 7 _aMAT002000
_2bisacsh
072 7 _aPBF
_2thema
082 0 4 _a512
_223
100 1 _aBiyikoğu, Türker.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aLaplacian Eigenvectors of Graphs
_h[electronic resource] :
_bPerron-Frobenius and Faber-Krahn Type Theorems /
_cby Türker Biyikoğu, Josef Leydold, Peter F. Stadler.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2007.
300 _aVIII, 120 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1915
505 0 _aGraph Laplacians -- Eigenfunctions and Nodal Domains -- Nodal Domain Theorems for Special Graph Classes -- Computational Experiments -- Faber-Krahn Type Inequalities.
520 _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.
650 0 _aAlgebra.
650 0 _aCombinatorics.
650 0 _aMatrix theory.
650 1 4 _aAlgebra.
_0http://scigraph.springernature.com/things/product-market-codes/M11000
650 2 4 _aCombinatorics.
_0http://scigraph.springernature.com/things/product-market-codes/M29010
650 2 4 _aLinear and Multilinear Algebras, Matrix Theory.
_0http://scigraph.springernature.com/things/product-market-codes/M11094
700 1 _aLeydold, Josef.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
700 1 _aStadler, Peter F.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540840664
776 0 8 _iPrinted edition:
_z9783540735090
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1915
856 4 0 _uhttps://doi.org/10.1007/978-3-540-73510-6
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c9306
_d9306