Question 7028 – UGC NET June-2019 CS Paper-2

Suppose that a connected planar graph has six vertices, each of degrees four. Into how many regions is the plane divided by a planar representation of this graph?

Correct Answer: B

Question 20 Explanation:

We apply Euler’s formula where r = e−v + 2.
Since each vertex has degree 4, the sum of the degrees is 24.
By the handshaking theorem, 2e = 24 .
so, e = 12.
r = 12−6 + 2
r = 8
Thus we have 8 regions in this planar graph.