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Number of Hamiltonian cycles in the graph C_n X C_n.
8

%I #28 Dec 30 2023 13:03:39

%S 48,1344,23580,3273360,257165468,171785923808,61997157648756,

%T 196554899918485160

%N Number of Hamiltonian cycles in the graph C_n X C_n.

%C C_n X C_n is also known as the (n,n)-torus grid graph.

%H Artem M. Karavaev, <a href="https://web.archive.org/web/20161024010518/http://flowproblem.ru/cycles/hamilton-cycles">Hamilton Cycles</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HamiltonianCycle.html">Hamiltonian Cycle</a>.

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

%t Table[Length[FindHamiltonianCycle[GraphProduct[CycleGraph[n], CycleGraph[n], "Cartesian"], All]], {n, 3, 6}] (* _Eric W. Weisstein_, Dec 16 2023 *)

%Y Cf. A270273, A003763, A222197, A268838, A222198, A193153, A270247.

%K nonn,hard,more

%O 3,1

%A _N. J. A. Sloane_, Feb 14 2013