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Eigenspaces of Graphs (Encyclopedia of Mathematics and its Applications, Series Number 66) - Hardcover

Book 49 of 188: Encyclopedia of Mathematics and its Applications

Cvetkovic, Dragos; Rowlinson, Peter; Simic, Slobodan

 
9780521573528: Eigenspaces of Graphs (Encyclopedia of Mathematics and its Applications, Series Number 66)
Hardcover
ISBN 10: 0521573521 ISBN 13: 9780521573528
Publisher: Cambridge University Press, 1997

Synopsis

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.

"synopsis" may belong to another edition of this title.

From the Back Cover

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).

"About this title" may belong to another edition of this title.

Publisher
Cambridge University Press
Publication date
1997
Language
English
ISBN 10 
0521573521
ISBN 13 
9780521573528
Binding
Hardcover
Edition number
1
Number of pages
276