Irredundance Polynomial

Let  be the number of irredundant sets of size  in a graph , then the irredundance polynomial  of  in the variable  is defined as

It may also be written as

where  is the upper irredundance number of  (cf. Burger et al. 1997, Mynhardt and Roux 2020).

REFERENCES

Burger, A. P.; Cockayne, E. J.; and Mynhardt, C. M. "Domination and Irredundance in the Queens' Graph." Disc. Math. 163, 47-66, 1997.

Mynhardt, C. M. and Roux, A. "Irredundance Graphs." 14 Apr. 2020. https://arxiv.org/abs/1812.03382.