1. Amusement park project
Module 1 Graph Theory

2. Part I – Euler Circuits
Due at the End of class on Thursday, September 27nd

3. Guidelines #1
Make a graph of all of the attractions and the paths between them that are described in the given table.
*extra credit offered for word processed document*
transfer each attraction to a vertex on a graph
label each attraction with letters
create a “key” naming each attraction
connect all of the vertices with edges according to the given table

4. Guidelines #1

5. Guidelines #2 Describe the valence of the graph.
Attraction
(vertex)
Valence
(original)
(change)
Splash
Mountain
Indiana
Jones
Adventure
Tarzan’s
Treehouse
Guidelines #2
Describe the valence of the graph.
for each vertex, describe the valence
if eulerization is needed, indicate change in valence

6. Guidelines #3 Create an Euler Circuit of the rides/attractions.
*Note that you may need to Eulerize the graph!*
describe the path that would be traveled by the guest
include order and direction (numbers & arrows)
if eulerization is needed, indicate edges added

7. Guidelines #4 What effect will this have on a guest at the park?
*Word processed document*
Discuss the paths the guests will have to take as a result of creating an Euler circuit of the graph of the park.
Describe in a few sentences the objectives of creating an Euler circuit.
Describe the benefits and any drawbacks of traveling an Euler circuit at the park.

8. Check the Rubric

9. Cover Page Requirements
Title of Project
Amusement Park Project Part I – Euler Circuits
Class Title
Math Applications & Reasoning
Graphic
Period
Group Member Names
First and last
Capitalization!

10. Part II – Hamiltonian Circuits
Due at the beginning of class on Friday, October 28th

11. Guidelines #1
Make a graph of all of the attractions and the paths connecting them; include the walking times along the edges, from the information given in the tables
Computer Generated or done on Poster Board

12. Guidelines #2
Use each of the algorithms discussed in the textbook to find an efficient (in terms of time) circuit of the rides.
Nearest-Neighbor
Starting at Splash Mountain
Sorted Edges

13. Guidelines #3
Compare the results of the algorithms you applied; what circuit takes the least amount of time.

14. Guidelines #4
Estimate the minimum time you would need at the amusement park to ride each attraction listed in these tables
Note you need to include the waiting/riding times in addition to the total walking time.
Must be word processed

15. Extra Credit Minimum Cost Spanning Tree A reason for finding the MSP
Use Kruskal’s Algorithm
Weights will be cost of MSP (thousands of dollars)
Include the spanning tree

16. Check the Rubric

17. Cover Page Required Title of Project Class Title Graphic Period
Amusement Park Project Part II – Hamiltonian Circuits
Class Title
Math Applications & Reasoning
Graphic
Period
Group Member Names
First and last
Capitalization!