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Let G be the non-planar graph with the minimum possible number of edges. Then G has
  • a)
    9 edges and 5 vertices
  • b)
    9 edges and 6 vertices
  • c)
    10 edges and 5 vertices
  • d)
    10 edges and 6 vertices
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Let G be the non-planar graph with the minimum possible number of edge...
For a simple, connected, planar graph with v vertices and e edges, the following simple conditions hold: If v ≥ 3 then e ≤ 3v − 6; Note that the question is about non-planar graph G. Only option C doesn't follow above.
Alternate Explanation: We know that K5 (which has 10 edges and 5 vertices) and K3,3K3,3 (which has 9 edges and 6 vertices) are non-planar graphs.
Since we are asked about minimum number of edges, answer should be k3,3k3,3 i.e. option (B) is correct. 
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Let G be the non-planar graph with the minimum possible number of edges. Then G hasa)9 edges and 5 verticesb)9 edges and 6 verticesc)10 edges and 5 verticesd)10 edges and 6 verticesCorrect answer is option 'C'. Can you explain this answer?
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