The upper irredundance number IR(G) of a graph G is the maximum size of an irredundant set of vertices in G. 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 G (Burger et al. 1997, Mynhardt and Roux 2020).
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