Answer:18
It follows from the Euler's formula that a simple planar graph G with m edges and n≥3 vertices must satisfy (see here)
m≤3n−6.(1)
For a graph G with m edges and n vertices, its complement G¯¯¯¯ has n(n−1)2−m edges. Therefore, if G¯¯¯¯ is also planar, by (1) we have
n(n−1)2−m≤3n−6.(2)
Adding (1) and (2), we obtain
n(n−1)2≤6n−12,
which implies that n≤10.
Explanation: