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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