|Course Archives Theoretical Statistics and Mathematics Unit|
Course: Graph Theory and Combinatorics
Time: Currently not offered
| Syllabus |
Syllabus : A course based on either of the following sequence of topics may be offered.
A 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 inclusionexclusion principle. Ramsey Theory: graphical and geometric.
B B.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, inclusionexclusion, Ram seys theorem, recurrence relations and generating functions. Time permitting, some of the following topics may be done: (i) strongly regular graphs, root systems, and classifica tion of graphs with least eigenvalue, (ii) Elements of coding theory (Macwilliams identity, BCH, Golay and Goppa codes, relations with designs).
Suggested Texts :
1. F. Harary, Graph Theory, Addision-Wesley (1969); Narosa (1988).
2. D.B. West, Introduction to Graph Theory, Prentice-Hall (1996); Indian ed (1999).
3. J.A. Bondy and U.S.R. Murty, Graph Theory with applications, Macmillan (1976).
4. H.J. Ryser, Combinatorial Mathematics, Carus Math Monographs; Math Assoc of America (1963).
5. M.J. Erickson, Introduction to Combinatorics, John Wiley (1996).
6. L. Lovasz, Combinatorial Problems and Exercises, AMS Chelsea (1979).
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