  The number of maximal independent sets of the n-cycle graph C_n is known to
be the nth term of the Perrin sequence. The action of the automorphism group of
C_n on the family of these maximal independent sets partitions this family into
disjoint orbits, which represent the non-isomorphic (i.e., defined up to a
rotation and a reflection) maximal independent sets. We provide exact formulas
for the total number of orbits and the number of orbits having a given number
of isomorphic representatives. We also provide exact formulas for the total
number of unlabeled (i.e., defined up to a rotation) maximal independent sets
and the number of unlabeled maximal independent sets having a given number of
isomorphic representatives. It turns out that these formulas involve both
Perrin and Padovan sequences.
