# Applications of parity formula on connected planar graph

I've been offered the adhering to trouble as homework:

```
A graph is drawn in the plane and has 78 faces, all of them triangles.
Prove the outer face is not a 19-gon.
```

We are additionally offered a tip to make use of the formula:|V|-|E|npls|F|= 2 (for planar, attached chart, where|F|= the variety of faces).

What I've attempted until now: I understand the variety of faces is 78, so I can connect "78" in for|F |. I understand there is possibly a means to compute|E|considered that the external face is a 19 - gon, yet I can not figure this out. Better, I visualize if I compute|E |, I'll locate that it does not please this formula which confirms the external face can not be a 19 - gon.

This is research, so I'm not seeking a solution or evidence. Could you offer some valuable tips to aim me in the appropriate instructions?

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Casey Patton 2022-07-25 20:47:06

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