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Eigenspaces of Graphs

Part of Encyclopedia of Mathematics and its Applications

  • Date Published: March 2008
  • availability: Available
  • format: Paperback
  • isbn: 9780521057189

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About the Authors
  • Graph theory is an important branch of contemporary combinatorial mathematics. By describing recent results in algebraic graph theory and demonstrating how linear algebra can be used to tackle graph-theoretical problems, the authors provide new techniques for specialists in graph theory. The book explains how the spectral theory of finite graphs can be strengthened by exploiting properties of the eigenspaces of adjacency matrices associated with a graph. The extension of spectral techniques proceeds at three levels: using eigenvectors associated with an arbitrary labeling of graph vertices, using geometrical invariants of eigenspaces such as graph angles and main angles, and introducing certain kinds of canonical eigenvectors by means of star partitions and star bases. Current research on these topics is part of a wider effort to forge closer links between algebra and combinatorics. Problems of graph reconstruction and identification are used to illustrate the importance of graph angles and star partitions in relation to graph structure. Specialists in graph theory will welcome this treatment of important new research.

    • First book to cover star partitions
    • Draws together a wide range of research
    • Authors are leading figures in graph theory
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    Reviews & endorsements

    "The overall level of writing is advanced, and the book is most suitable for research specialists in graph theory." Telegraphic Reviews

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    Product details

    • Date Published: March 2008
    • format: Paperback
    • isbn: 9780521057189
    • length: 276 pages
    • dimensions: 234 x 156 x 15 mm
    • weight: 0.39kg
    • contains: 77 b/w illus. 4 tables
    • availability: Available
  • Table of Contents

    1. A background in graph spectra
    2. Eigenvectors of graphs
    3. Eigenvectors of techniques
    4. Graph angles
    5. Angle techniques
    6. Graph perturbations
    7. Star partitions
    8. Canonical star bases
    9. Miscellaneous results.

  • Authors

    Dragos Cvetkovic, Univerzitet u Beogradu, Yugoslavia

    Peter Rowlinson, University of Stirling

    Slobodan Simic, Univerzitet u Beogradu, Yugoslavia

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