Multiple choice general knowledge science & technology

If G is a connected planar graph with e edges,v vertices,and f faces then which is true?

  1. f=v-e+2

  2. f=e-v+2

  3. f=e+v-2

  4. f=e-v-2
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B Correct answer
Explanation

Euler's formula for connected planar graphs states v - e + f = 2, where v is vertices, e is edges, and f is faces. Rearranging gives f = e - v + 2. This fundamental relationship applies to all connected planar graphs drawn without edge crossings.

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