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For a connected planar simple graph G=(V, E) with e=|E|=16 and v=|V|=9, then find the number of regions that are created when drawing a planar representation of the graph?

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For a connected planar simple graph G=(V, E) with e=|E|=16 and v=|V|=9, then find the number of regions that are created when drawing a planar representation of the graph?

(a) 321

(b) 9

(c) 1024

(d) 596

I have been asked this question during an internship interview.

My question is taken from Planarity, Degree and Coloring of Graph in section Graphs of Discrete Mathematics

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The correct choice is (b) 9

The best explanation: Note that K3,3 and K5 are the “smallest” non-planar graphs because in that every non-planar graph contains them. According to Kuratowski’s theorem, a graph is defined as non-planar if and only if it contains a subgraph homomorphic to K3,3 or K5.

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