The upper irredundance number 
of a graph 
is the maximum size of an irredundant
set of vertices in 
. It is therefore equal to the size of a maximum
irredundant set as well to the size of a maximal
irredundant set since every maximum irredundant
set is also maximal. The upper irredundance number is also equal to largest exponent
in an irredundance polynomial.
The (lower) irredundance number may be similarly defined as the minimum size of a maximal irredundant
set of vertices in 
(Burger et al. 1997, Mynhardt and Roux 2020).
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).
