000 | 03294nam a22005175i 4500 | ||
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001 | 978-3-540-73510-6 | ||
003 | DE-He213 | ||
005 | 20190213151035.0 | ||
007 | cr nn 008mamaa | ||
008 | 100301s2007 gw | s |||| 0|eng d | ||
020 |
_a9783540735106 _9978-3-540-73510-6 |
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024 | 7 |
_a10.1007/978-3-540-73510-6 _2doi |
|
050 | 4 | _aQA150-272 | |
072 | 7 |
_aPBF _2bicssc |
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072 | 7 |
_aMAT002000 _2bisacsh |
|
072 | 7 |
_aPBF _2thema |
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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. |
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300 |
_aVIII, 120 p. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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338 |
_aonline resource _bcr _2rdacarrier |
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347 |
_atext file _bPDF _2rda |
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490 | 1 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v1915 |
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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 |
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