Description 
1 online resource (viii, 115 pages) : illustrations 
Series 
Lecture notes in mathematics, 00758434 ; 1915 

Lecture notes in mathematics (SpringerVerlag) ; 1915.

Contents 
Graph Laplacians  Eigenfunctions and Nodal Domains  Nodal Domain Theorems for Special Graph Classes  Computational Experiments  FaberKrahn Type Inequalities 
Summary 
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 wellstudied 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 
Bibliography 
Includes bibliographical references (pages 101114) and index 
Notes 
Print version record 
Subject 
Eigenvectors.


Laplacian operator.


Graph theory.


Teoría de grafos


Laplace, Operador de


Eigenvectors


Graph theory


Laplacian operator

Form 
Electronic book

Author 
Leydold, Josef.


Stadler, Peter F., 1965

ISBN 
9783540735106 

3540735100 

3540735097 

9783540735090 
