A connected planar graph having 6 vertices, and 7 edges contains _____, regions.a)15b)3c)1d)11
Question
A connected planar graph having 6 vertices, and 7 edges contains _____, regions.a)15b)3c)1d)11
Solution
The number of regions in a connected planar graph can be calculated using Euler's formula, which states that:
V - E + F = 2
where V is the number of vertices, E is the number of edges, and F is the number of faces (regions).
Given that the graph has 6 vertices (V = 6) and 7 edges (E = 7), we can substitute these values into Euler's formula to find the number of regions:
6 - 7 + F = 2
Solving for F, we get:
F = 2 - 6 + 7 = 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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