Counting nonisomorphic maximal independent sets of the ncycle graph
Abstract
The number of maximal independent sets of the ncycle 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 nonisomorphic (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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 January 2007
 arXiv:
 arXiv:math/0701647
 Bibcode:
 2007math......1647B
 Keywords:

 Mathematics  Combinatorics;
 Computer Science  Discrete Mathematics;
 Mathematics  Group Theory;
 05C69;
 05C38;
 05C25 (Primary) 05A15;
 05A17;
 11Y55 (Secondary)
 EPrint:
 Revised version