1. Graph Concepts and Algorithms Using LEDA By Caroline Moore and Carmen Frerichs (252a-at and 252a-ao) each graph in the presentation was created using gw_basic_graph_algorithms

2. 1. Vertices, Edges vertex edge

3. 2. Multiple Edges, Loops Multiple edge loop

4. 3. Undirected Graph

5. 4. Directed Graph

6. 5. Simple Graph A simple graph has no multiple edges and no loops.

7. 6. Examples of graphs and multigraphs This is both a graph and a multigraph (multigraph is a graph containing multiple edges) Multiple edge

8. 7. Special classes of graphs: complete A complete graph is one in which each node is connected to every other node.

9. 7b. Special classes of graphs: bipartite A bipartite graph has two or more classes. Vertices cannot connect within their own class. Class AClass B

10. 8. Planar Graphs A planar graph has no crossed edges.

11. 11. Subgraph of a Graph Original Graph Subgraph: Induced Subgraph:

12. 13. Path in an undirected graph A path is a collection of edges which connect nodes in a graph without creating cycles.

13. 14. Path in a directed graph

14. 15. Hamilton Path in an undirected graph A Hamilton Path is a path which connects all of the vertices in a graph without creating a cycle.

15. 16. Hamilton path is an directed graph

16. 17. Cycle in an undirected graph A cycle is a path in which all vertices have degree 2.

17. 18. Cycle in an undirected graph

18. 19. Hamilton cycle in an undirected graph A Hamilton cycle is a cycle connecting all vertices in a graph.

19. 20. Hamilton cycle in a directed graph

20. 28. Cyclic and acyclic digraph A cyclic digraph An acyclic digraph

21. 38. Tree A tree is an acyclic connected graph.

22. 39. Forest A forest is a graph containing multiple trees