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
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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