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A351335
Number of unlabeled directed graphs on n nodes without a subgraph isomorphic to directed K_{2,2} that have the maximal number of edges (=A191873(n)).
1
1, 1, 1, 1, 6, 5, 4, 829, 707, 2938, 55779, 60084
OFFSET
1,5
COMMENTS
When adjacency matrices viewed as those of bipartite graphs, these bipartite graphs are pairwise isomorphic for each n <= 12, except for n = 5 and n = 8 with 2 and 3 distinct bipartite graphs, respectively.
EXAMPLE
For n = 7 there are 4 such graphs with A191873(7) = 21 edges, described by the following adjacency matrices:
[0111000] [0110100] [0110010] [0010101]
[1010100] [1011000] [1000011] [1001001]
[1100010] [1000101] [0101001] [0100011]
[0100101] [1100010] [1100100] [1010010]
[0010011] [0010011] [1011000] [0111000]
[1001001] [0101001] [0010101] [1100100]
[0001110] [0001110] [0001110] [0001110]
Absence of directed K_{2,2} subgraph means that these matrices do not contain a rectangle with four 1s at the corners.
CROSSREFS
Unlabeled version of A191874.
Directed version of A335820.
Cf. A191873.
Sequence in context: A291068 A019131 A019132 * A021862 A199375 A244808
KEYWORD
nonn,more
AUTHOR
Max Alekseyev, Feb 07 2022
STATUS
approved