Irredundance Polynomial

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

It may also be written as

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

See also

Irredundance Number, Irredundant Set, Upper Irredundance Number

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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.

Referenced on Wolfram|Alpha

Irredundance Polynomial

Cite this as:

Weisstein, Eric W. "Irredundance Polynomial." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/IrredundancePolynomial.html

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