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Authored Book

Eigenspaces of Graphs

Citation
Cvetkovic D, Rowlinson P & Simic S (1997) Eigenspaces of Graphs. Encyclopedia of Mathematics and its Applications, 66. Cambridge: Cambridge University Press. http://www.cambridge.org/gb/academic/subjects/mathematics/discrete-mathematics-information-theory-and-coding/eigenspaces-graphs

Abstract
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.

StatusPublished
Author(s)Cvetkovic, Dragos; Rowlinson, Peter; Simic, Slobodan
Title of seriesEncyclopedia of Mathematics and its Applications
Number in series66
Publication date31/12/1997
PublisherCambridge University Press
Publisher URLhttp://www.cambridge.org/…genspaces-graphs
Place of publicationCambridge
ISBN9780521057189
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