Laplacian Eigenvectors of Graphs Perron Frobenius and Faber Krahn Type Theorems

Description

Publisher: Springer
Language: English
ISBN: 3540735097
Paperback: 120 pages
Data: Sep 2007
Format: PDF
Description: 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 Schr?dinger 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.



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