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 a 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).
