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A370198
Number of maximum independent vertex sets in the n X n antelope graph.
1
1, 1, 1, 1, 1, 1, 8, 4, 4, 4, 4, 4, 1, 2, 290
OFFSET
1,7
LINKS
Eric Weisstein's World of Mathematics, Antelope Graph.
Eric Weisstein's World of Mathematics, Maximum Independent Vertex Set.
MATHEMATICA
Table[Length@With[{g = RelationGraph[Sort[Abs[Subtract[##]]] == {3, 4} &, Tuples[Range[n], {2}]]}, FindIndependentVertexSet[g, Length /@ FindIndependentVertexSet[g], All]], {n, 8}]
PROG
(Python)
from collections import Counter
from networkx import empty_graph, find_cliques, complement
def A370198(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 ((3, 4), (3, -4), (-3, 4), (-3, -4), (4, 3), (4, -3), (-4, 3), (-4, -3)) if 0<=i+k<n and 0<=j+l<n)
return (x:=Counter(len(c) for c in find_cliques(complement(G))))[max(x)] # Chai Wah Wu, Feb 12 2024
CROSSREFS
Sequence in context: A197033 A245720 A229495 * A131921 A129105 A226276
KEYWORD
nonn,more,hard
AUTHOR
Eric W. Weisstein, Feb 11 2024
STATUS
approved