

Contents


Week 1: 
preliminary results on linear algebra and graph theory 
Week 2: 
Matrices associated to a graph , The spectrum of a graph

Week 3: 
The spectrum of some graphs , The complete graph ,The complete bipartite graph

Week 4: 
The cycle , The path , Line graphs ,Cartesian products

Week 5: 
Strongly regular graphs , The spectrum of an undirected graph 
Week 6: 
Regular graphs , Spanning trees 
Week 7: 
Characterization by spectra , Cospectral graphs

Week 8: 
Midterm Exam 
Week 9: 
Structure and one eigenvalue, Star complements

Week 10: 
Graphs with least TWO eigenvalues , Spectral techniques 
Week 11: 
Spectrum and graph structure, Authomorphisms and eigenspaces

Week 12: 
Distance regular graphs , Laplacian, 
Week 13: 
Laplacian spectrum, The matrixtree theorem

Week 14: 
Algebraic connectivity , Laplacian eigenvalues and graph structure 
Week 15*: 
Expansion , Graph automorphism 
Week 16*: 
Final Exam 
Textbooks and materials: 
Topics in Algebraic Graph Theory; W. Beineke and R.J. Wilson, 2004. 
Recommended readings: 
• Algebraic Graph Theory; C. Godsil and G. Royle, 2001. • Algebraic Graph Theory; N. Biggs, 1993. • Spectra of Graphs; D. Cvetkovic, M. Doob and Sachs, 1995.


* Between 15th and 16th weeks is there a free week for students to prepare for final exam.

