NAVIGATING AN AMUSEMENT PARK
Graph Theory Assessment Project
PART I – EULER CIRCUITS
1. Make a graph of all of the attractions and the paths between them that are described in the
given tables.
2. Determine and record the valence of each vertex in the graph.
3. Create an Euler Circuit of the rides/attractions. Clearly show your starting point and number
your route. (Note that you may need to eulerize the graph!)
4. Describe in a few sentences what the value of knowing this circuit would be to you at the park.
Also explain what the real-world meaning is if you had to eulerize the graph.
PART II – HAMILTONIAN CIRCUITS
1. Make a graph of all of the attractions and paths connecting them (use the same layout from
Part I); include walking times along the edges, from the information given in the tables.
2. Use the Nearest Neighbor method starting from the ride with the largest valance to find an
efficient (in terms of time) circuit of the rides. Remember that for any vertex with a valance of
two those two edges must be used. Show Nearest Neighbor route on graph.
3. Use the Sorted-Edges method to find an efficient (in terms of time) circuit of the rides. Show
work for Sorted-Edges.
4. Compare the results of the two methods; what circuit takes the least amount of time?
5. Estimate the minimum time you would need at Disneyland to ride each attraction listed in
these tables. (Note: You need to include the waiting/riding times in addition to the total walking
time.)
6. Describe in a few sentences what the value of knowing this circuit would be to you at the park.
7. When visiting Disneyland would knowing an Euler Circuit or Hamiltonian Circuit be more
important? Why?