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Review for Exam 2 Attempted Answers:

tfields

My first attempt to upload this was a fail. Anyway, I am not to great at these graphs so please correct me where I am wrong. I also did not figure out number 9.

tfields

My #2(C) should be (5,4,4,3,3,3,2)

ssatterw

If you haven’t found the answer to 9 yet here’s how I did it. I counted the number of faces by writing the numbers within them as I counted and got 39 faces. Then I noticed that all the vertices have degree 4. And since we know the sum of all of the vertices degrees equals 2e and we’re told the graph has 36 vertices I multiple 4 by 36 to get 144 and divided that by 2 to get e=72. Then plugging that into Euler’s formula v-e+f=2, 36-72+39, -36+39=3 therefore it can’t be planar.

Correction:
v-e+f=2 doesn’t always prove planar, but e \leq 3v-6 does and 144 \nleq 3(36) -6 3*36 = 108 -6 =102 and 144 \nleq 102