Eigenspaces of Graphs

This book describes the spectral theory of finite graphs.

Dragos Cvetkovic (Author), Peter Rowlinson (Author), Slobodan Simic (Author)

9780521057189, Cambridge University Press

Paperback / softback, published 1 March 2008

276 pages, 77 b/w illus. 4 tables
23.4 x 15.5 x 1.5 cm, 0.398 kg

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

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.

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.

Subject Areas: Combinatorics & graph theory [PBV]