let x be the no. of vertices to be calculated.

According to the Handshaking lemma ,

The sum of degree of all the vertices = 2* |E|

6 * 2 + 3 * 4 + (x-9) * 3 = 2 * 27

→ 12 + 12 + 3x – 27 = 54

→ 24 + 3x = 54 + 27

→ 3x = 54 + 27 – 24

→ 3x = 57

→ x = 19

So , the no. of vertices is (D) 19