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# Independent Dominating Set

An independent dominating set of a graph is a set of vertices in that is both an independent vertex set and a dominating set of . Independent dominating sets are equivalent to maximal independent vertex sets.

The minimum size of an independent dominating set in a graph is known as its independent domination number (Crevals and Östergård 2015, Ilić and Milošević 2017). Since any maximal independent vertex set is also a minimal dominating set (Mynhardt and Roux 2020), the independent domination number is equivalent to the lower independence number.

## See also

Dominating Set, Independent Vertex Set, Lower Independence Number

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## References

Crevals, S. and Östergård, P. R. J. "Independent Domination of Grids." Disc. Math. 338, 1379-1384, 2015.Ilić, A. and Milošević, M. "The Parameters of Fibonacci and Lucas Cubes." Ars Math. Contemp. 12, 25-29, 2017.Mynhardt, C. M. and Roux, A. "Irredundance Graphs." 14 Apr. 2020. https://arxiv.org/abs/1812.03382.

## Cite this as:

Weisstein, Eric W. "Independent Dominating Set." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/IndependentDominatingSet.html