The discrete version of a continuous surface
sampled at optimum sampling rate can be well
expressed in form of a neighborhood graph containing
the critical points (maxima, minima, saddles) of
the surface. Basic operations on the graph such as
edge contraction and removal eliminate non-critical
points and collapse plateau regions resulting in the
formation of a graph pyramid. If the neighborhood
graph is well-composed, faces in the graph pyramid
are slope regions. In this paper we focus on the graph
on the top of the pyramid which will contain critical
points only, self-loops and multiple edges connecting
the same vertices. We enumerate the different
possible configurations of slope regions, forming a
catalogue of different configurations when combining
slope regions and studying the number of slope
regions on the top
