A284707 Number of maximal independent vertex sets in the n-hypercube graph Q_n.

1, 2, 2, 6, 42, 1670, 1281402

Offset: 0

Author

Eric W. Weisstein, Apr 01 2017

Keywords

• nonn
• more

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, Independent Vertex Set
• Eric Weisstein's World of Mathematics, Maximal Independent Vertex Set

Crossrefs

Cf. A027624 (not necessarily maximal), A366425 (non-isomorphic).

Programs

Mathematica

Table[Length @ FindIndependentVertexSet[HypercubeGraph[n], Infinity, All], {n, 0, 6}] (* Eric W. Weisstein, Jan 01 2024 *)

Python

from networkx import empty_graph, find_cliques
def A284707(n):
    k = 1<Chai Wah Wu, Jan 11 2024

Formula

a(n) ~ 2*n*2^(N/4) where N = 2^n [Kahn and Park]. - N. J. A. Sloane, Sep 11 2019