A286882
Number of minimal dominating sets in the n X n knight graph.
Original entry on oeis.org
1, 1, 14, 243, 2686, 161458
Offset: 1
A303155
Number of total dominating sets in the n X n knight graph.
Original entry on oeis.org
0, 0, 0, 15625, 7210119, 7595819716, 38315570995200, 907603926752600100, 90471688044300692000805, 36477409490805834487688340121, 57078206407327794909123594938975856, 349529784665230581716185532814423836231824, 8484852661962127775820139948519390269746327643440
Offset: 1
A290785
Number of irredundant sets in the n X n knight graph.
Original entry on oeis.org
2, 16, 150, 5771, 270411, 51462132
Offset: 1
A291099
Number of maximal irredundant sets in the n X n knight graph.
Original entry on oeis.org
1, 1, 14, 277, 7796, 478904
Offset: 1
A291705
Number of connected dominating sets in the n X n knight graph.
Original entry on oeis.org
1, 0, 0, 11140, 6635521, 7249082465, 35733685780960
Offset: 1
A289201
Number of maximal independent vertex sets (and minimal vertex covers) in the n X n knight graph.
Original entry on oeis.org
1, 1, 10, 31, 172, 2253, 50652, 900243, 26990541, 1534414257
Offset: 1
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Table[Length[FindIndependentVertexSet[KnightTourGraph[n, n], Infinity, All]], {n, 7}]
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from networkx import empty_graph, find_cliques, complement
def A289201(n):
G = empty_graph((i,j) for i in range(n) for j in range(n))
G.add_edges_from(((i,j),(i+k,j+l)) for i in range(n) for j in range(n) for (k,l) in ((1,2),(1,-2),(-1,2),(-1,-2),(2,1),(2,-1),(-2,1),(-2,-1)) if 0<=i+kChai Wah Wu, Jan 11 2024
Showing 1-6 of 6 results.