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) 596I 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

For a connected planar simple graph G=(V, E) with e=|E|=16 and v=|V|=9

1.	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) 596I 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
Answer» 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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