The (lower) irredundance number 
of a graph 
is the minimum size of a maximal
irredundant set of vertices in 
.
The upper irredundance number is defined as the maximum size of an irredundant set of vertices
in 
(Burger et al. 1997, Mynhardt and Roux 2020). In other words, it is the size
of a maximum irredundant set, which is
the same as the maximum size of a maximal irredundant
set since all maximum irredundant sets are also maximal.
The (lower) irredundance number 
, (lower) domination number 
, lower
independence number 
, upper independence
number 
,
upper domination number 
, and upper
irredundance number 
satsify the chain of inequalities
 |
(Burger et al. 1997).
