  With this work we aim to show how Mathematica can be a useful tool to
investigate properties of combinatorial structures. Specifically, we will face
enumeration problems on independent subsets of powers of paths and cycles,
trying to highlight the correspondence with other combinatorial objects with
the same cardinality. Then we will study the structures obtained by ordering
properly independent subsets of paths and cycles. We will approach some
enumeration problems on the resulting partially ordered sets, putting in
evidence the correspondences with structures known as Fibonacci and Lucas
Cubes.
