2. [6 marks]. Consider the following graph:

(i) If G had a planar drawing, how many faces would it have?

(ii) If G had a planar drawing, what would the be the sum of the face degrees?

(iii) What can you conclude from (ii) and (iii)? [Recall that in a planar drawing of a simple graph,

each face has degree at least three.]

(iv) Do you think G has a planar drawing?

In each part of this question, be sure to give a brief justification of how you got your answer; answers

without justification will not receive any marks.