1 Phone Lines
1. (5 pts)
You are running a business with several offices in different towns. You are
going to lease phone lines to connect them with each other. The price that
the phone company charges is different between different pairs of towns.
Find the set of lines that connects all your offices with a minimum total
cost. Show your reasoning. The towns are A, B, C, D, and E. The prices
per unit distance are shown on the edges.
B
5
C
3
2
4
F
9
6
8
A
D
9
7
E
2. (2 pts) Demonstrate that the graph above is a planar graph and
demonstrate that Euler's formula is correct for the graph.
