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English
Cambridge University Press
23 October 2008
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.

By:   , , ,
Imprint:   Cambridge University Press
Country of Publication:   United Kingdom
Volume:   66
Dimensions:   Height: 234mm,  Width: 155mm,  Spine: 15mm
Weight:   398g
ISBN:   9780521057189
ISBN 10:   0521057183
Series:   Encyclopedia of Mathematics and its Applications
Pages:   276
Publication Date:  
Audience:   Professional and scholarly ,  Undergraduate
Format:   Paperback
Publisher's Status:   Active

Reviews for Eigenspaces of Graphs

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