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).
https://www.isibang.ac.in/~adean/infsys/database/MMath/GT.html