  For a planar graph with a given f-vector $(f_{0}, f_{1}, f_{2}),$ we
introduce a cubic polynomial whose coefficients depend on the f-vector. The
planar graph is said to be real if all the roots of the corresponding
polynomial are real. Thus we have a bipartition of all planar graphs into two
disjoint class of graphs, real and complex ones. As a contribution toward a
full recognition of planar graphs in this bipartition, we study and recognize
completely a subclass of planar graphs that includes all the connected grid
subgraphs. Finally, all the 2-connected triangle-free complex planar graphs of
7 vertices are listed.
