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If G is a simple graph with 15 edges and $\bar{G}$ has 13 edges, how many vertices does G have?
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May be @Psunny wants to ask the question this way...

If a graph G has 15 edges and G' (G-bar) has 13 edges. How many Vertices does G has .?

To answer this question we know that G U G' is Complete Graph Kn

Therefore G+G' = 15+13 = 28

Total number of edges in the complete graph is nC2

nC2 = (n(n-1))/2 = 28 

By solving the equation we get n= 8 or -7 

therefore the number of vertices, n = 8 

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