  We prove that the complement of a non-separating planar graph of order at
least nine is intrinsically linked. We also prove that the complement of a
non-separating planar graph of order at least 10 is intrinsically knotted. We
show these lower bounds on the orders are the best possible. We show that for a
maximal non-separating planar graph with $n\ge 7$ vertices, its complement $cG$
is $(n-7)-$apex. We conclude that the de Verdi\`ere invariant for such graphs
satisfies $\mu(cG)\le n-4$.
