On the Connectivity of Maximal Planar Graphs with Minimum Degree 5

Let Fn,k, be the classes of maximal planar graphs Gn (without loops or multiple edges) having k vertices of degree 5 and n-k vertices of degree more than 5. Hakimi and Schmeichel proved that if Gn ɛ Fn,k and k=12, 13, then Gn is 5-connected. In this paper the author gives some general conditions in terms of the integers n and k for a graph Gn ɛ Fn,k to be p-connected, with p=4,5.