M2a
Suppose you wish to plan a trip, starting in Lincoln, visiting Blair, Fremont, Hastings
and Lexington in some order, and then returning to Lincoln. The following is a table
of distances between these cities:
Blair
Blair
Fremont
Hastings
Lexington
Fremont
24
Hastings
159
137
Lexington
211
190
89
Lincoln
66
53
101
166
A. Draw (neatly) a complete graph with the five cities at the vertices, and label each
edge with the distance between the two cities.
B. How many different trips (circuits) are there (starting and finishing in Lincoln)?
Explain.
C. Which circuit do you believe is the shortest? How many miles is it? How did you
decide on this circuit? Check your work with your neighbor. Show the shortest circuit
on the graph in Part A.
D. Suppose you have been hired as a consultant to connect all five cities together with
a computer cable. Use Kruskal’s algoritm to find the way to do this using the least
amount of cable. Show your work below, and show the network on the graph in Part
A. How many miles of cable are needed?