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.
No because Eulers formula does not add up to 2
- 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)
Correct, for the reason you gave.