Let G= (V (G), E (G) ) be a simple graph. A set D V (G) is a strong dominating set of G, if for every vertex x V (G) D there is a vertex y D with xy E (G) and deg (x) deg (y). The strong domination number ₒₓ (G) is defined as the minimum cardinality of a strong dominating set. In this paper, we calculate ₒₓ (G) for specific graphs and study the number of strong dominating sets of some graphs.
Zaherifar et al. (2023) studied this question.