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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.

MSC:
05C50Graphs and linear algebra
90C22Semidefinite programming
90C27Combinatorial optimization
90C35Programming involving graphs or networks
05C90Applications of graph theory