A semikernel of a directed graph is an independent vertex set 
such that every graph vertex outside 
reached by a directed edge
from 
has a directed
edge back to some member of 
(Neumann-Lara 1971, Galeana-Sánchez and Neumann-Lara
1984).
Chvátal and Lovász (1974) used the name "semi-kernel" for what is now called a quasi-kernel. In a consistently oriented cycle graph on three vertices, each singleton set is a quasi-kernel, while the empty set is the only semikernel.
