Counting non-isomorphic maximal independent sets of the n-cycle graph
English
Bisdorff, Raymond[University of Luxembourg > Faculty of Law, Economics and Finance > Applied Mathematics Unit (SMA)]
Marichal, Jean-Luc[University of Luxembourg > Faculty of Law, Economics and Finance > Applied Mathematics Unit (SMA)]
Jan-2007
1
No
No
International
21st Annual Conf. of the Belgian Operational Research Society (ORBEL 21), Luxembourg, Jan. 18-19, 2007
from 18-01-2007 to 19-01-2007
Raymond Bisdorff
Claude Lamboray
Jean-Luc Marichal
Patrick Meyer
Luxembourg
Luxembourg
[en] maximal independent set ; cycle graph ; combinatorial enumeration ; dihedral group ; group action ; cyclic and palindromic composition of integers ; Perrin and Padovan sequences
[en] It is known that the number of maximal independent sets of the $n$-cycle graph $C_n$ is given by the $n$th 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 unlabelled (i.e., defined up to a rotation) maximal independent sets and the number of unlabelled maximal independent sets having a given number of isomorphic representatives. It turns out that these formulas involve both Perrin and Padovan sequences.
University of Luxembourg - UL
Recherches méthodologiques et mathématiques en aide à la décision et à la classification > 01/01/2005 – 12/12/2007 > BISDORFF Raymond
[University of Luxembourg > Faculty of Law, Economics and Finance > Applied Mathematics Unit (SMA)]
