A290607 Number of maximal independent vertex sets (and minimal vertex covers) in the n-Keller graph.
1, 56, 1712, 46336, 1570048, 76425216
Offset: 1
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
Programs
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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
Extensions
a(5) from Eric W. Weisstein, Nov 05 2018
a(6) from Chai Wah Wu, Jan 11 2024