A296527 Number of (undirected) cycles in the n X n torus grid graph.

312, 14704, 2183490, 995818716, 1383238940818, 5846378997135040, 75162787766308673244

Offset: 3

Author

Eric W. Weisstein, Dec 14 2017

Keywords

• nonn
• more

Links

• Eric Weisstein's World of Mathematics, Graph Cycle.
• Eric Weisstein's World of Mathematics, Torus Grid Graph.

Crossrefs

Cf. A222199, A268838.

Programs

Mathematica

Table[Length[FindCycle[GraphProduct[CycleGraph[n], CycleGraph[n], "Cartesian"], Infinity, All]], {n, 3, 5}] (* Eric W. Weisstein, Dec 16 2023 *)

Python

# Using graphillion
from graphillion import GraphSet
def make_CnXCk(n, k):
    grids = []
    for i in range(1, k + 1):
        for j in range(1, n):
            grids.append((i + (j - 1) * k, i + j * k))
        grids.append((i + (n - 1) * k, i))
    for i in range(1, k * n, k):
        for j in range(1, k):
            grids.append((i + j - 1, i + j))
        grids.append((i + k - 1, i))
    return grids
def A296527(n):
    universe = make_CnXCk(n, n)
    GraphSet.set_universe(universe)
    cycles = GraphSet.cycles()
    return cycles.len()
print([A296527(n) for n in range(3, 7)])  # Seiichi Manyama, Nov 22 2020

Extensions

a(7) from Andrew Howroyd, Dec 14 2017

a(8)-a(9) from Ed Wynn, Jun 28 2023