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Number of maximal independent vertex sets in the n X n torus grid graph.
1

%I #27 Jan 26 2024 10:14:36

%S 1,2,6,42,220,3644,62272,1794762,83280570,6210321492

%N Number of maximal independent vertex sets in the n X n torus grid graph.

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

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TorusGridGraph.html">Torus Grid Graph</a>.

%t Table[Length@FindIndependentVertexSet[GraphProduct[CycleGraph[n], CycleGraph[n], "Cartesian"], Infinity, All], {n, 3, 8}] (* _Eric W. Weisstein_, Jan 26 2024 *)

%o (Python)

%o from networkx import find_cliques, complement, cartesian_product, cycle_graph

%o def A321250(n): return sum(1 for c in find_cliques(complement(cartesian_product(cycle_graph(n),cycle_graph(n))))) # _Chai Wah Wu_, Jan 11 2024

%Y Cf. A027683.

%K nonn,more

%O 1,2

%A _Eric W. Weisstein_, Nov 01 2018

%E a(1), a(2), and a(10) from _Andrew Howroyd_, Nov 01 2018