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Consider the following hexagon with the shown vertices connected:

Wheel graph

We now add additional connections:

i) e is connected to b

ii) c is connected to d

ii) a is connected to f

How many ways can we color each point either red, white, or blue such that connected points have different colors?

I am HORRIBLE bad with these problems. I was thinking casework but I cannot seem to ensure I have all the cases.

4 Answers 4