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Number of maximal independent vertex sets (and minimal vertex covers) in the n-Keller graph.
+10
2
1, 56, 1712, 46336, 1570048, 76425216
OFFSET
1,2
LINKS
Eric Weisstein's World of Mathematics, Keller Graph
Eric Weisstein's World of Mathematics, Maximal Independent Vertex Set
Eric Weisstein's World of Mathematics, Minimal Vertex Cover
PROG
(Python)
from itertools import zip_longest
from sympy.ntheory.factor_ import digits
from networkx import empty_graph, find_cliques
def A290607(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 (s:=tuple(c-d&3 for c, d in zip_longest(digits(a, 4)[-1:0:-1], digits(b, 4)[-1:0:-1], fillvalue=0))).count(2)==0 or s.count(0)>len(s)-2)
return sum(1 for c in find_cliques(G)) # Chai Wah Wu, Jan 11 2024
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Eric W. Weisstein, Aug 07 2017
EXTENSIONS
a(5) from Eric W. Weisstein, Nov 05 2018
a(6) from Chai Wah Wu, Jan 11 2024
STATUS
approved
Number of independent vertex sets and vertex covers in the n-Keller graph.
+10
1
16, 393, 26705, 18843905, 4403212671745
OFFSET
1,1
LINKS
Eric Weisstein's World of Mathematics, Independent Vertex Set
Eric Weisstein's World of Mathematics, Keller Graph
Eric Weisstein's World of Mathematics, Vertex Cover
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Eric W. Weisstein, Apr 04 2017
EXTENSIONS
a(5) from Andrew Howroyd, Mar 20 2018
STATUS
approved

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