Choose the correct alternatives ( more than one may be correct) and write the corresponding letters only:
(viii) A non-planar graph with minimum number of vertices has
(a) 9 edges, 6 vertices
(b) 6 edges, 4 vertices
(c) 10 edges, 5 vertices
(d) 9 edges, 5 vertices
A non-planar graph with minimum number of vertices has 10 edges, 5 vertices i.e K5
A non-planar graph with minimum number of edges has 9 edges, 6 vertices i.e K3,3
Answer: C
Using Planarity criteria relation $e \leq 3\times v -6,$
All other option satisfies this relation except option $(C)$
i.e$10 \nleqslant 3 \times 5-6$
sir , I think it is not sufficient condition..because for K_{3,3} , 9<= 3*6 - 6 but it is non-planar graph..please correct me if I m wrong..