Upper Irredundance Number
المؤلف:
Burger, A. P.; Cockayne, E. J.; and Mynhardt, C. M.
المصدر:
"Domination and Irredundance in the Queens Graph." Disc. Math. 163
الجزء والصفحة:
...
4-5-2022
1944
Upper Irredundance Number
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).
REFERENCES
Burger, A. P.; Cockayne, E. J.; and Mynhardt, C. M. "Domination and Irredundance in the Queens' Graph." Disc. Math. 163, 47-66, 1997.
Cockayne, E. J. and Mynhardt, C. M. "The Sequence of Upper and Lower Domination, Independence and Irredundance Numbers of a Graph." Disc. Math. 122, 89-102, 1993).
Hedetniemi, S. T. and Laskar, R. C. "A. Bibliography on Dominating Sets in Graphs and Some Basic Definitions of Domination Parameters." Disc. Math. 86, 257-277, 1990.
Mynhardt, C. M. and Roux, A. "Irredundance Graphs." 14 Apr. 2020. https://arxiv.org/abs/1812.03382.
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