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These are the major topics to be covered on the first test. Most topics require foundational and background knowledge.|
1. Bipartite graphs. A characterization of bipartite graphs.|
2. Isomorphism of graphs.
3. Representations of graphs: adjacency and incidence matrices.
4. Eulerian circuits and trails. Euler Theorem.
5. Extremal problems on graphs. Mantel's Theorem.
6. Graphic sequences. A theorem on such sequences.
7. Directed graphs: degrees, connectivity, Eulerian circuits, de Bruijn graphs.
8. Tournaments, kings in tournaments.
9. Trees, characterizations of trees.
10. Centers of trees.
11. Prufer codes, Cayley's formula.
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