> 
> Draw a planar graph with two vertices of degree 3 and four vertices of degree 5, if possible.
> 
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**Attempt**:

With handshaking lemma, I get this:

$2e = 26 \implies e=13$

Then with Euler's formula, I get:

$6-13+f=2 \implies f = 9$

However, since $e \leq 3v - 6$ for a simple, connected, planar graph I would get:

$13 \leq 3(6)-6$

$13 \leq 12$

I can't figure out how I could get 9 faces for my graph. I can only get 8 faces as shown here:

[![enter image description here](https://i.stack.imgur.com/NgC4r.png)](https://i.stack.imgur.com/NgC4r.png)

This is the best attempt I had on this problem with no success.