1. UNIT 1: EULER CIRCUITS
GRAPH THEORY

2. TURNING MAPS INTO GRAPHS

5. TURNING GRAPHS INTO MAPS

7. Definitions
Valence: The number of edges meeting at a vertex is considered the vertex’s valence.
Circuit: A connected series of edges that starts and ends at the same vertex (special path).

8. Label the valences of all of the vertices of the following graph:

9. Declare whether or not the following graphs are circuits:B C D

10. Definition:
Euler Circuit: A circuit that covers every edge of a graph exactly one time.

11. Find (if possible) the Euler Circuit

12. Find (if possible) the Euler Circuit:

13. Literacy Practice
Read section 1.3 starting on page 11 and finishing on page 12.

14. Eulerization
Graphs are Euler circuits when ___________________________.
Eulerizing a graph is when EDGES are added to the graph until an Euler circuit exists.

15. What is the minimum number of edges needed to eulerize the following graphs:

16. Minimum number of edges to Eulerize
The minimum number of edges needed to Eulerize a graph is based on the following equation: (# odd valences)/2

17. Eulerize the following graphs with the fewest edges possible.

18. Draw a small map of a city and have your neighbor draw a graph that represents and efficient route around that city. You will be required to complete this on the test, so use this time wisely to practice.

19. Jobs that use Euler Circuits:
Trash Collection Companies
Political Candidates
Delivery Services (Post Office, FedEx, UPS, etc.)
Yard maintenance services
Warehouse operators
Police officers
More