Module 8 Activity: Traveling Effectively
This module activity will use your knowledge from Module 7 and Module 8. You may need to review important terminology
Choose four states or countries to which you would like to travel. Use an atlas, a newspaper, or an online travel site for your
research. Created a weighted graph of these places and your own state that shows either a) the number of miles between each
state and every other states or b) the cost of an airplane (or if you prefer, train or bus) ticket from every place to every other.
Your graph should be a complete, weighted graph with five vertices, including your own state.
Work through the following and provide images for each of the graphs when asked. How can I upload an image? Go here.
1. Draw the graph here. (Remember that it's OK for lines to cross, but be as neat as possible.)
2. Find an Euler circuit on your graph. You can start and end at the vertex of your choice. Draw that circuit here. (Remember, we
are looking for an Euler circuit, not a Hamilton circuit.)
3. Use the nearest-neighbor algorithm to find the approximately cheapest or shortest way to start from home, visit each place,
and return home. Draw the circuit here. List the cost/weight of your circuit.
4. Explain how you used the nearest-neighbor algorithm to find the cheapest way. What vertex did you go to first, and why?
Second? Third? Why?
5. Using the correct formula, how many Hamilton circuits are in your graph? Show your work.
6. Use the cheapest link algorithm to find the approximately cheapest or shortest way to start from home, visit each place, and
return home. Draw the circuit here. List the cost/weight of your circuit.
7. Explain how you used the cheapest link algorithm to find the cheapest way. How did you determine your vertices and why?
