GATE 2012 CS (CS1) – Question 27

A connected simple planar graph has ten vertices and fifteen edges. How many bounded faces does any plane embedding have?

Show answer and explanation

Correct answer: (D) 6

Explanation

Euler’s formula V−E+F=2 counts all faces including the unbounded exterior. Hence F=2−10+15=7. Removing the exterior gives six bounded faces, D.

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