UGC-NET | NTA UGC NET 2019 June – II | Question 20

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?
(A) 6
(B) 8
(C) 12
(D) 10

Answer: (B)
Explanation:
We know that,the sum of the degree of vertices = 2 * number of edges (handshaking theorem)
=> e=12

Also according to Euler’s formula,
=> r = e−v+2
=> r = 12−6+2
=> r =12−6+2
=> r = 8

So Option 2 is correct.
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