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Eigenspaces of Graphs by Dragos M. Cvetkovic, Peter Rowlinson, Slobodan Simic
  

Synopsis

Eigenspaces of Graphs by Dragos M. Cvetkovic, Peter Rowlinson, Slobodan Simic

Current research on the spectral theory of finite graphs may be seen as part of a wider effort to forge closer links between algebra and combinatorics (in particular between linear algebra and graph theory).This book describes how this topic 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 labelling 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. One objective is to describe graphs by algebraic means as far as possible, and the book discusses the Ulam reconstruction conjecture and the graph isomorphism problem in this context. Further 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.

Reviews

'Specialists in graph theory and mathematical chemistry will welcome this treatment of important new research.'
European Mathematical Society

About the Author

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Book Info

Publication date

22nd December 2007

Author

Dragos M. Cvetkovic, Peter Rowlinson, Slobodan Simic

More books by Dragos M. Cvetkovic, Peter Rowlinson, Slobodan Simic
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Publisher

Cambridge University Press

Format

Paperback
276 pages

Categories

Combinatorics & graph theory

ISBN

9780521057189

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