Is it possible to find an upper bound for the number of edges in a simple planar graph with n vertices?
To be more specific, if we represent the number of vertices and number of edges as an ordered pair, then $(3,3), (4,6), (5,9)$ have planar representations. What is the highest number of edges for which a graph with 6 vertices have a planar representation? Is it possible to generalise this to n vertices?