| Eigenspaces of Graphs Contributor(s): Cvetkovic, Dragos (Author), Rowlinson, Peter (Author), Simic, Slobodan (Author) |
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ISBN: 1139086545 ISBN-13: 9781139086547 Publisher: Cambridge University Press OUR PRICE: $140.25 Product Type: Open Ebook - Other Formats Published: December 2011 |
| Additional Information |
| BISAC Categories: - Mathematics | Discrete Mathematics - Mathematics | Graphic Methods |
| Dewey: 511.5 |
| Series: Encyclopedia of Mathematics and Its Applications |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |