Spectra of Graphs
In Spring 2006, Andries E. Brouwer and Willem H. Haemers gave a
series of lectures at IPM, the Institute for Studies in Theoretical
Physics and Mathematics in Tehran. The lecture notes were combined
and published as an IPM report. Since that time, various versions
of that text have been available at this site.
Preprint PDF.
A book version was released by Springer on the 16th of December 2011.
However, the copyright year is 2012.
A.E. Brouwer & W.H. Haemers,
Spectra of graphs,
Springer,
New York, etc., 2012.
ISBN 978-1-4614-1938-9.
Book Errata
p. 55, 3rd line following Step 4: semibipartite should be split.
Additions
On p. 37, line 2 a conjecture (by Nikiforov) on the sum of the spectral
radii of a graph and its complement is mentioned. This conjecture has
now been proved by Lingsheng Shi.
On p. 210 it says: One might wonder whether the disjoint union of
regular DS graphs with the same degree is always DS.
Wonder no more! Both
2K3,3 + Σ ⊗ K2 and
3(C6 □ K2)
are bipartite cubic graphs with spectrum
±33 ±26 ±13 012.
