If there are five faces and nine vertices in an undirected planar graph, then…

2023

If there are five faces and nine vertices in an undirected planar graph, then number of edges is

Answer: C. 12 — For a connected planar graph, Euler's formula states V - E + F = 2. Given vertices (V) = 9 and faces (F) = 5, we substitute these values: 9 - E + 5 = 2.…

  1. A.

    14

  2. B.

    16

  3. C.

    12

  4. D.

    none of the above

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Correct answer: C

For a connected planar graph, Euler's formula states V - E + F = 2. Given vertices (V) = 9 and faces (F) = 5, we substitute these values: 9 - E + 5 = 2. Simplifying gives 14 - E = 2, so E = 12.

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