A287225
Number of matchings in the n X n knight graph.
Original entry on oeis.org
1, 1, 47, 8617, 4437215, 18283403428, 478131755555352, 65146261730656227552, 51516890628947512147926356, 244151636345172523021724077440553, 6697138334086551576618194527162685383161
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
-
Table[Length[FindIndependentVertexSet[KnightTourGraph[n, n], Infinity, All]], {n, 7}]
-
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
A289202
Number of maximum matchings in the n X n knight graph.
Original entry on oeis.org
1, 1, 2, 16, 644, 10304, 65113608, 2849759680, 118928612871184, 58888109421793792
Offset: 1
-
Join[{1, 1}, Table[Length[With[{g = LineGraph[KnightTourGraph[n, n]]}, FindIndependentVertexSet[g, Length /@ FindIndependentVertexSet[g], All]]], {n, 3, 5}]]
Showing 1-3 of 3 results.