|Course Archives Theoretical Statistics and Mathematics Unit|
Course: Graph Theory and Combinatorics
Time: Currently not offered
| Syllabus |
i) Construction and Uniqueness of Finite Fields, Linear Codes, Macwilliams identity, Finite projective planes, strongly regular graphs and regular 2-graphs. t designs with emphasis on Mathieu designs. Counting arguments and inclusion exclusion principle. Ramsey Theory: graphical and geometric.
ii) Graphs and digraphs, connectedness, trees, degree sequences, connectivity, Eulerian and Hamiltonian graphs, matchings and SDRs, chromatic numbers and chromatic index, planarity, covering numbers, flows in networks, enumeration, Inclusion exclusion, Ramseys theorem, recurrence relations and generating functions.
iii) Time permitting, some of the following topics may be done: (i) strongly regular graphs, root systems, and classification of graphs with least eigenvalue, (ii) Elements of coding theory (Macwilliams identity, BCH, Golay and Goppa codes, relations with designs).
Suggested Texts :
(a) F. Harary, Graph Theory, Addision-Wesley (1969), Narosa (1988).
(b) D. B. West, Introduction to Graph Theory, Prentice-Hall (Indian Edition 1999).
(c) J. A. Bondy and U. S. R. Murthy, Graph Theory and Applications, MacMillan (1976).
(d) H. J. Ryser, Combinatorial Mathematics, Carus Math. Monograph, MAA (1963).
(e) M. J. Erickson, Introduction to Combinatorics, John Wiley (1996).
(f) L. Lovasz, Combinatorial Problems and Exercises, AMS Chelsea (1979).
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