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A290606
Number of maximal independent vertex sets (and minimal vertex covers) in the n-halved cube graph.
3
1, 2, 4, 4, 40, 136, 8080, 17331120
OFFSET
1,2
LINKS
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
KEYWORD
nonn,more
AUTHOR
Eric W. Weisstein, Aug 07 2017
STATUS
approved