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Graph Laplacians. (English) Zbl 1161.05334

Beineke, Lowell W. (ed.) et al., Topics in algebraic graph theory. Cambridge: Cambridge University Press (ISBN 0-521-80197-4/hbk). Encyclopedia of Mathematics and Its Applications 102, 113-136 (2004).
This is Chapter 4 of the first in a planned new series of books surveying individual areas of graph theory, each being a collection of articles written by experts from within a particular area. In this case the area is algebraic graph theory.
Section headings are as follows: Introduction; The Laplacian of a graph; Laplace eigenvalues; Eigenvalues and vertex partitions of graphs; The max-cut problem and semidefinite programming; Isoperimetrixc inequalities; The travelling salesman problem; Random walks on graphs.
For the entire collection see [Zbl 1052.05003].

MSC:

05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
90C22 Semidefinite programming
90C27 Combinatorial optimization
90C35 Programming involving graphs or networks
05C90 Applications of graph theory
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