# Lecture 12 Graph Concepts and Algorithms

1. Vertices, edges.
2. Multiple edges. Loops.
3. (Undirected) Graph.
4. Directed Graph(digraph).
5. Simple graph.
6. Examples of graphs and multigraphs.
7. Special classes of graphs: complete, bipartite.
8. Planar Graphs: example.
9. Non-planar graph: example.
10. Drawing graphs: an example for each graph layout implemented in LEDA.
11. Subgraph of a graph.
12. Subgraph of a directed graph.
13. Path in an undirected graph.
14. Path in a directed graph.
15. Hamilton path in an undirected graph.
16. Hamilton path in a directed graph.
17. Cycle in an undirected graph
18. Cycle in a directed graph
19. Hamilton cycle in an undirected graph
20. Hamilton cycle in a directed graph
21. Connected graph.
22. A graph which is not connected.
23. Spanning tree of a graph which is connected.
24. Spanning forest of a graph which is not connected.
25. Connected component.
26. An example of a subgraph which is connected but is not a connected component.
27. Decomposition of a graph which is not connected into connected components.
28. Cyclic and acyclic digraph.
29. Partial order.
30. Total order.
31. Acyclic graphs vs. partial orders. Hasse diagrams.
32. Transitive closure of a digraph.
33. Strongly connected digraph.
34. A graph which is not strongly connected.
35. A strongly connected component in a digraph (the digraph should NOT be strongly connected).
36. An example of a subgraph of a digraph which is strongly connected but is not a strongly connected component.
37. The decomposition of a digraph into strongly connected components.
38. Tree.
39. Forest.
40. Articulation (cut) point in an undirected graph.
41. Biconnected graph.
42. An example of a graph which is biconnected.
43. An example of a graph which is NOT biconnected.
44. An example of a graph with two articulation points.
45. The "cactus" decomposition of a connected graph into biconnected components.
46. Traversal of graphs and digraphs.
47. Depth-first search.