(math 5301(Introduction to Discrete Structures

 Content

1. Graphs, Directed graphs, Basic definitions,
2. Isomorphism of graphs, Sub graphs, Paths and cycles 
3. Matrix representations of graphs.
4. Connectedness, Bridges, Cut-vertices
5. Trees, Spanning trees, Weighted graphs and minimum spanning trees.
6. Shortest paths, Eulerian circuits, Hamiltonian cycles.
7. Tournaments, Applications.
8. Planar graphs, Euler's Formula, Kuratowski's theorem
9. Graph coloring, Vertex coloring, Edge coloring, Map coloring, Chromatic polynomials.
10. Ordered sets, Comparability and covering graphs
11. Dilworth theorem,
12.Block designs, Latin squares, Orthogonal Latin squares