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.

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.