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Number of maximal independent vertex sets in the n-Lucas cube graph.
1

%I #17 Feb 16 2025 08:34:06

%S 1,2,2,4,17,64,731,43388,20087577

%N Number of maximal independent vertex sets in the n-Lucas cube graph.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LucasCubeGraph.html">Lucas Cube Graph</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MaximalIndependentVertexSet.html">Maximal Independent Vertex Set</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MinimalVertexCover.html">Minimal Vertex Cover</a>

%o (Python)

%o from itertools import product, combinations

%o from networkx import empty_graph, find_cliques

%o def A367681(n):

%o v = tuple(int(q,2) for q in (''.join(p) for p in product('01',repeat=n)) if '11' not in q+q[0])

%o G = empty_graph(v)

%o e = tuple((a,b) for a, b in combinations(v,2) if (lambda m: (m&-m)^m if m else 1)(a^b))

%o G.add_edges_from(e)

%o return sum(1 for c in find_cliques(G)) # _Chai Wah Wu_, Jan 11 2024

%K nonn,more,changed

%O 1,2

%A _Eric W. Weisstein_, Nov 26 2023