Let i_k(G) be the number of irredundant sets of size k in a graph G, then the irredundance polynomial R_G(x) of G in the variable x is defined as R_G(x) = sum_(k = 1)^( left bracketing bar V(G) right bracketing bar ) i_k(G) x^k. It may also be written as R_G(x) = sum_(k = 1)^(IR(G)) i_k(G) x^k, where IR(G) is the upper irredundance number of G (cf. Burger et al. 1997, Mynhardt and Roux 2020).

irredundance number | irredundant set | upper irredundance number