1. SECTION 5.1: Euler Circuit Problems

2. What is a routing problem?
Routing problems deal with finding ways to deliver goods and/or services to many different destinations. Does a possible route exist or which one of the possible routes is the most efficient?
Examples of routing problems: delivering mail, walking through a neighborhood…

3. The Seven Bridges of Konigsberg: A prize is offered to the first person who can find a way to walk across each one of the seven bridges of Konigsberg without re-crossing any and return to the original starting point.
bridge

4. SECTION 5.2: GRAPHS

5. A graph is a picture consisting of vertices (dots) and edges (lines)
A graph is a picture consisting of vertices (dots) and edges (lines). The edges do not have to be straight lines but they have to connect two vertices.
Example: or

6. A loop is an edge connecting a vertex back with itself.
This is a loop named BB
No loop

7. An isolated vertex is the vertex that is not connected to any other vertex.
Vertex F is an isolated vertex

8. Multiple edges have two vertices for which there exists more than one edge connecting them.
These are multiple edges CD or DC

9. Disconnected graph: a graph made up of connected pieces Example:
Components - pieces of disconnected graphs which are themselves connected G

10. List vertex set and edge set
Vertex set V =
Edge set E =

11. Example Consider the graph with V={A, B, C, D, E}
and E={AC, AE, BD, BE, CA, CD, CE, DE}
Draw several different pictures of the graph.