Various characterizations of throttling numbers

Zero forcing can be described as a graph process that uses color change rule in which vertices white to blue. The throttling number of minimizes the sum initially colored blue and time steps required entire graph. Positive semidefinite (PSD) zero is commonly studied variant standard alters rule. This paper introduces method for extending using PSD process. Using this extension method, graphs with at most t are characterized specific minors Cartesian product complete trees. A similar characterization obtained minor monotone floor forcing. Finally, set connected on n least − k by forbidding finite family induced subgraphs. These forbidden subgraphs constructed throttling.