Counting non-isomorphic maximal independent sets of the n-cycle graph

Raymond Bisdorff; Jean-Luc Marichal

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arXiv · math/0701647

Counting non-isomorphic maximal independent sets of the n-cycle graph

Raymond Bisdorff·Jean-Luc Marichal

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Abstract

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.

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BibTeX RIS

Raymond Bisdorff, Jean-Luc Marichal. 2008-12-15. Counting non-isomorphic maximal independent sets of the n-cycle graph. https://arxiv.org/abs/math/0701647

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