| Eigenspaces of Graphs Contributor(s): Cvetkovic, Dragos (Author), Rowlinson, Peter (Author), Simic, Slobodan (Author) |
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ISBN: 0521573521 ISBN-13: 9780521573528 Publisher: Cambridge University Press OUR PRICE: $134.90 Product Type: Hardcover - Other Formats Published: January 1997 Annotation: This book describes 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 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. Current research on these topics 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). |
| Additional Information |
| BISAC Categories: - Mathematics | Graphic Methods - Mathematics | Discrete Mathematics |
| Dewey: 511.5 |
| LCCN: 96002860 |
| Series: Encyclopedia of Mathematics and Its Applications |
| Physical Information: 0.69" H x 6.14" W x 9.21" (1.24 lbs) 276 pages |
| 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. |