## Trending News

Anonymous

# Possible for a planar graph to have 6 vertices, 10 edges and split the plane into 5 regions (including the infinite region)?

This is one of my final exam review questions I want to make confirm with someone if my answer is right.

My solution:

v-e+f=2

v-e+f=2

6-10+5=1

No because Eulers formula does not add up to 2

### 1 Answer

Relevance

- PuzzlingLv 71 month agoFavorite Answer
A (connected) planar graph must satisfy Euler's formula:

v - e + f = 2

Since those numbers do not satisfy Euler's formula, it isn't possible.

6 - 10 + 5 = 1 (not 2)

Answer:

Correct, for the reason you gave.

- Login to reply the answers

Still have questions? Get your answers by asking now.