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A343648
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Triangle read by rows, 1 <= k <= n: T(n,k) is the number of (unlabeled) connected graphs with n nodes and zero forcing number k.
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2
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1, 1, 0, 1, 1, 0, 1, 4, 1, 0, 1, 10, 9, 1, 0, 1, 33, 58, 19, 1, 0, 1, 94, 457, 266, 34, 1, 0, 1, 319, 3977, 5574, 1184, 61, 1, 0, 1, 1053, 39547, 142039, 72944, 5393, 102, 1, 0, 1, 3683, 414891, 4170606, 5919941, 1180610, 26668, 170, 1, 0
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OFFSET
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1,8
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COMMENTS
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The zero forcing number of a graph can be defined as follows. Start with a blue/white coloring of the nodes. At each step, all white nodes, which are currently the unique white neighbor of a blue node, are colored blue. The zero forcing number is the minimum number of blue nodes in an initial coloring that leads to all nodes being blue after a finite number of steps.
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LINKS
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FORMULA
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T(n,1) = 1. (The path graph is the only n-node graph with zero forcing number 1.)
T(n,n-1) = 1 for n >= 2. (The complete graph is the only connected n-node graph with zero forcing number n-1.)
T(n,n) = 0 for n >= 2.
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EXAMPLE
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Triangle begins:
n\k 1 2 3 4 5 6 7 8 9 10
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1: 1
2: 1 0
3: 1 1 0
4: 1 4 1 0
5: 1 10 9 1 0
6: 1 33 58 19 1 0
7: 1 94 457 266 34 1 0
8: 1 319 3977 5574 1184 61 1 0
9: 1 1053 39547 142039 72944 5393 102 1 0
10: 1 3683 414891 4170606 5919941 1180610 26668 170 1 0
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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