Largest planar graphs and largest maximal planar graphs of diameter two (Q1612379)

The maximum number of vertices in a planar graph with diameter \(k\) and maximum degree \(\Delta\) is considered. The maximum number of vertices in a maximal planar graph (i.e. a planar graph which has an embedding in the plane so that every face is a triangle) with diameter \(k\) and maximum degree \(\Delta\) is also considered. The exact maximum number of vertices in a planar graph and a maximal planar graph with diameter 2 and maximum degree \(\Delta< 8\) is computed, too.