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A simple connected planar graph with $6$ vertices and $12$ edges. How do we show that each of the face is bounded by three edges?

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2 Answers

Hint: how many faces are there? Then each one has a minimum of three edges in its boundary.

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You should have learned about Euler's formula

$p-q+f=2$ $p$ - vertices $q$ - edges $f$ - faces

You can use that result to show each face has 3 edges, look at 7.4.2


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