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
- 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
- Decomposition of a graph which is not connected into
- 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.
- 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
- Traversal of graphs and digraphs.
- Depth-first search.
- Breadth-first search.