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A connected planar graph having 6 vertices, 7 edges contains _____________ regions.Select one:a.15b.3c.1d.11

Question

A connected planar graph having 6 vertices, 7 edges contains _____________ regions.

Select one:

  • a. 15
  • b. 3
  • c. 1
  • d. 11
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Solution

The number of regions (R) in a connected planar graph can be calculated using the formula:

R = E - V + 2

where E is the number of edges and V is the number of vertices.

In this case, E = 7 (the number of edges) and V = 6 (the number of vertices).

Substituting these values into the formula gives:

R = 7 - 6 + 2 = 3

So, a connected planar graph having 6 vertices and 7 edges contains 3 regions. Therefore, the correct answer is b. 3.

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