MCZA048-14 Spectral Graph Theory (4-0-4)
Syllabus:
Matrices associated to graphs. Perron-Frobenius’ Theorem and the Espectral Theorem for symmetric, nonnegative, real matrices. Cauchy’s Interlacing Theorem. Rayleigh’s Principle. Spectra of certain graphs and
graph classes such as paths, cycles and trees. Spectra of subgraphs. Spectra, connectivity and diameter.
Chromatic number, independence number, maximum clique and its estimates based on the spectra.
Spectral techniques in graph algorithms. Expander graphs and applications in computer science.
Recommendation:
Linear Algebra; Graph Theory.
Required texts:
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1. D. Cvetkovic, P. Rowlison, S. Simic, An introduction to the theory of graph spectra. Cambridge
University Press, 2010. ISBN-13: 978-0-5211-3408-8.
● 2. C. Godsil, G. Royle, Algebraic graph theory. Springer, 2001.
ISBN-13: 978-0-3879-5241-3.
● 3. Andries E. Brouwer, Willem H. Haemers. Spectra of Graphs. Springer-Verlag New York.
ISBN-13: 978-1-4899-9433-2.
Additional texts:
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1. Lubotzky, Discrete groups, expanding graphs and invariant measures. Birkhauser Verlag, 2010.
ISBN-13: 9783034603317.
2. Piet Van Mieghem, Graph Spectra for Complex Network. Cambridge University Press New York, NY,
2011.
ISBN-13: 978-0-5211-9458-7
3. Fan Chung e Linyuan Lu,Complex Graphs and Networks. American Mathematical Society CBMS
Regional Conference Series in Mathematics, 2006. ISBN-13: 978-0-8218-3657-6
4. Fan R. K. Chung, Spectral Graph Theory (CBMS Regional Conference Series in Mathematics, No. 92),
American Mathematical Society, 1996.
ISBN-13: 978-0-8218-0315-8.
5. Alexander Lubotzky, Discrete groups, expanding graphs and invariant measures. Birkhauser Verlag,
2010.
ISBN-13: 978-3-0346-0331-7.