Submodular functions and M-convex sets

This paper covers a few simple examples of submodular functions with the proof of their submodularity. All examples relate to graphs, and we will examine the similarities between the different submodular functions. Furthermore, the paper covers M-convex sets. It shows for some submodular functions that the lattice points can be interpreted differently. The paper gives proofs and algorithms to obtain the alternative definition, of the lattice points from the M-convex sets of the cut and coverage functions.