OFFSET
1,8
COMMENTS
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.
LINKS
Shaun M. Fallat, Leslie Hogben, Jephian C.-H. Lin, and Bryan L. Shader, The inverse eigenvalue problem of a graph, zero forcing, and related parameters, Notices of the American Mathematical Society 67 (2020), 257-261.
FORMULA
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.
EXAMPLE
Triangle begins:
n\k 1 2 3 4 5 6 7 8 9 10
------------------------------------------------------------------
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
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Pontus von Brömssen, Apr 24 2021
STATUS
approved