A290606 Number of maximal independent vertex sets (and minimal vertex covers) in the n-halved cube graph.

1, 2, 4, 4, 40, 136, 8080, 17331120

Offset

1,2

Links

Table of n, a(n) for n=1..8.

Eric Weisstein's World of Mathematics, Halved Cube Graph.

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

Eric Weisstein's World of Mathematics, Minimal Vertex Cover.

Mathematica

Table[Length@FindIndependentVertexSet[GraphPower[HypercubeGraph[n - 1], 2], Infinity, All], {n, 7}]

Prog

(Python)
from networkx import empty_graph, find_cliques, complement, power
def A290606(n):
    k = 1<<n-1
    G = empty_graph(range(k))
    G.add_edges_from((a, b) for a in range(k) for b in range(a) if (lambda m: not(m&-m)^m if m else False)(a^b))
    return sum(1 for c in find_cliques(complement(power(G, 2)))) # Chai Wah Wu, Jan 11 2024

Crossrefs

Cf. A288943.

Sequence in context: A225171 A320600 A360685 * A155952 A277445 A145636

Adjacent sequences: A290603 A290604 A290605 * A290607 A290608 A290609

Keyword

nonn,more

Author

Eric W. Weisstein, Aug 07 2017

Status

approved