  The inverse degree of a graph is the sum of the reciprocals of the degrees of
its vertices. We prove that in any connected planar graph, the diameter is at
most 5/2 times the inverse degree, and that this ratio is tight. To develop a
crucial surgery method, we begin by proving the simpler related upper bounds
(4(V-1)-E)/3 and 4V^2/3E on the diameter (for connected planar graphs), which
are also tight.
