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- W2952248883 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." @default.
- W2952248883 created "2019-06-27" @default.
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- W2952248883 date "2007-01-23" @default.
- W2952248883 modified "2023-09-27" @default.
- W2952248883 title "Counting non-isomorphic maximal independent sets of the n-cycle graph" @default.
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