Fall 2000

Ileana Streinu

Graph Concepts and Algorithms

**Vertices, edges.****Multiple edges. Loops.****(Undirected) Graph.****Directed Graph(digraph).****Simple graph.****Examples of graphs and multigraphs.****Special classes of graphs: complete, bipartite.**- Planar Graphs: example.
- Non-planar graph: example.
- Drawing graphs: an example for each graph layout implemented in LEDA.
- Subgraph of a graph.
- Subgraph of a directed graph.
**Path in an undirected graph.****Path in a directed graph.****Hamilton path in an undirected graph.****Hamilton path in a directed graph.****Cycle in an undirected graph****Cycle in a directed graph****Hamilton cycle in an undirected graph****Hamilton cycle in a directed graph**- Connected graph.
- A graph which is not connected.
- Spanning tree of a graph which is connected.
- Spanning forest of a graph which is not connected.
- Connected component.
- An example of a subgraph which is connected but is not a connected component.
- Decomposition of a graph which is not connected into connected components.
**Cyclic and acyclic digraph.**- Partial order.
- Total order.
- Acyclic graphs vs. partial orders. Hasse diagrams.
- Transitive closure of a digraph.
- Strongly connected digraph.
- A graph which is not strongly connected.
- A strongly connected component in a digraph (the digraph should NOT be strongly connected).
- An example of a subgraph of a digraph which is strongly connected but is not a strongly connected component.
- The decomposition of a digraph into strongly connected components.
**Tree.****Forest.**- Articulation (cut) point in an undirected graph.
- Biconnected graph.
- An example of a graph which is biconnected.
- An example of a graph which is NOT biconnected.
- An example of a graph with two articulation points.
- The "cactus" decomposition of a connected graph into biconnected components.
- Traversal of graphs and digraphs.
- Depth-first search.
- Breadth-first search.