Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

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

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  • 1 month ago
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    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.

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