The 
-forcing
number 
of a finite simple graph 
, for a positive integer 
, is the smallest size of an initial colored vertex
set that eventually colors the whole graph under the
following rule. A colored vertex with at most 
uncolored neighbors
colors all of them. The case 
is the zero forcing number.
Abiad et al. (2026) proved that 
for every such graph 
and positive
integers 
and 
, where 
is a graph power.
