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Positive Semidefinite Zero Forcing Number


The positive semidefinite zero forcing number Z_+(G) of a graph G is the minimum size of an initially colored vertex set that colors the whole graph by the positive semidefinite forcing rule. At each step, delete the colored vertices to form uncolored connected components. A colored vertex may color its unique uncolored neighbor within any one such component, regardless of its uncolored neighbors in other components.

Abiad et al. (2026) proved monotonicity under successive graph powers, Z_+(G^r)<=Z_+(G^(r+1)) for every r>=1.


See also

Zero Forcing Number, Zero Forcing Set

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References

Abiad, A.; Flagg, M.; Ghasemi Nezhad, S.; and Zeijlemaker, S. "The Zero Forcing Number of Graph Powers." 2 Oct 2026. https://arxiv.org/abs/2610.03892.

Cite this as:

Weisstein, Eric W. "Positive Semidefinite Zero Forcing Number." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PositiveSemidefiniteZeroForcingNumber.html

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