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Interlacing eigenvalues and graphs. (English) Zbl 0831.05044
A survey paper to various kinds of applications of eigenvalue interlacing to matrices associated with graphs. Bounds are obtained for characteristic numbers of graphs, such as the size of maximal (co)clique, the chromatic number, the diameter, and the bandwidth, in terms of the eigenvalues of the standard adjacency matrix or the Laplacian matrix. The paper also deals with inequalities and regularity results concerning the structure of graphs and block designs.

MSC:
05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
05B05 Combinatorial aspects of block designs
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