A366425 Number of inequivalent maximal independent vertex sets in the n-hypercube graph Q_n.

1, 2, 2, 4, 10, 62, 3385

Offset: 0

Author

Dmitry I. Ignatov, Oct 09 2023

Keywords

• nonn
• more
• hard

Comments

a(n) is the number of orbits for the corresponding families of maximal independent vertex sets in the n-hypercube graph Q_n (see also A284707) under the action of the symmetry group S_n.

Examples

			a(0) = 1 since {0} is the only maximal independent vertex set of Q_0, which is the graph consisting of a single vertex labeled 0.
a(1) = 2 since Q_1 = 0---1 has maximal independent vertex sets {0} and {1}, which are inequivalent.
		

Links

• Dwight Duffus, Peter Frankl, and Vojtěch Rödl, Maximal independent sets in bipartite graphs obtained from Boolean lattices, European Journal of Combinatorics 32.1 (2011): 1-9.
• Dwight Duffus, Peter Frankl, and Vojtěch Rödl, Maximal independent sets in the covering graph of the cube, Discrete Applied Mathematics 161.9 (2013): 1203-1208.
• Dmitry I. Ignatov, On the Maximal Independence Polynomial of the Covering Graph of the Hypercube up to n = 6, Int'l Conf. Formal Concept Analysis, 2023.
• Liviu Ilinca and Jeff Kahn, Counting maximal antichains and independent sets, arXiv:1202.4427 [math.CO], Feb 2012; Order 30.2 (2013): 427-435.
• Jeff Kahn and Jinyoung Park, The number of maximal independent sets in the Hamming cube, arXiv:1909.04283 [math.CO], 2019.
• Eric Weisstein's World of Mathematics, Hypercube Graph.
• Eric Weisstein's World of Mathematics, Maximal Independent Vertex Set.

Crossrefs

Cf. A027624, A284707.