Eigenspaces of Graphs

by Dragos Cvetkovic, Peter Rowlinson, Slobodan Simic

Overview

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.

Product Details

ISBN-13:	9780521057189
Publisher:	Cambridge University Press
Publication date:	03/01/2008
Series:	Encyclopedia of Mathematics and its Applications , #66
Pages:	276
Product dimensions:	6.10(w) x 9.21(h) x 0.59(d)

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.

Editorial Reviews

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

From the Publisher