Geodesic
The Slater and Sub-k-Domination Number of a Graph with Applications to Domination and k-Domination
Discussiones Mathematicae. Graph Theory, Tome 40 (2020) no. 1, pp. 209-225

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In this paper we introduce and study a new graph invariant derived from the degree sequence of a graph G, called the sub-k-domination number and denoted subk(G). This invariant serves as a generalization of the Slater number; in particular, we show that subk(G) is a computationally efficient sharp lower bound on the k-domination number of G, and improves on several known lower bounds. We also characterize the sub-k-domination numbers of several families of graphs, provide structural results on sub-k-domination, and explore properties of graphs which are subk(G)-critical with respect to addition and deletion of vertices and edges.
Keywords: Slater number, domination number, sub- k -domination number, k -domination number, degree sequence index strategy 
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Amos, David; Asplund, John; Brimkov, Boris; Davila, Randy. The Slater and Sub-k-Domination Number of a Graph with Applications to Domination and k-Domination. Discussiones Mathematicae. Graph Theory, Tome 40 (2020) no. 1, pp. 209-225. http://geodesic.mathdoc.fr/item/DMGT_2020_40_1_a13/