Interlacing eigenvalues and graphs

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Abstract

We give several old and some new applications of eigenvalue interlacing to matrices associated to graphs. Bounds are obtained for characteristic numbers of graphs, such as the size of a 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. We also deal with inequalities and regularity results concerning the structure of graphs and block designs.
Original languageEnglish
PublisherUnknown Publisher
VolumeFEW 675
Publication statusPublished - 1994

Publication series

NameResearch memorandum / Tilburg University, Department of Economics
VolumeFEW 675

Fingerprint

Interlacing
Graph Design
Eigenvalue
Characteristic numbers
Laplacian Matrix
Block Design
Adjacency Matrix
Graph in graph theory
Chromatic number
Clique
Regularity
Bandwidth
Standards

Keywords

  • Graphs
  • Eigenvalues
  • mathematics

Cite this

Haemers, W. H. (1994). Interlacing eigenvalues and graphs. (Research memorandum / Tilburg University, Department of Economics; Vol. FEW 675). Unknown Publisher.
Haemers, W.H. / Interlacing eigenvalues and graphs. Unknown Publisher, 1994. (Research memorandum / Tilburg University, Department of Economics).
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Haemers, WH 1994, Interlacing eigenvalues and graphs. Research memorandum / Tilburg University, Department of Economics, vol. FEW 675, vol. FEW 675, Unknown Publisher.

Interlacing eigenvalues and graphs. / Haemers, W.H.

Unknown Publisher, 1994. (Research memorandum / Tilburg University, Department of Economics; Vol. FEW 675).

Research output: Book/ReportReportProfessional

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AB - We give several old and some new applications of eigenvalue interlacing to matrices associated to graphs. Bounds are obtained for characteristic numbers of graphs, such as the size of a 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. We also deal with inequalities and regularity results concerning the structure of graphs and block designs.

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Haemers WH. Interlacing eigenvalues and graphs. Unknown Publisher, 1994. (Research memorandum / Tilburg University, Department of Economics).