Eigenspaces of Graphs. (Encyclopedia of mathematics and its applications, vol.66) - Hardcover

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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).