Abstract The d -distance p -packing domination number dᵖ (G) γ d p (G) of a graph G is the cardinality of a smallest set of vertices of G which is both a d -distance dominating set and a p -packing. If no such set exists, then we set dᵖ (G) = γ d p (G) = ∞. For an arbitrary strong product G H G ⊠ H it is proved that ₃ᵖ (G H) dᵖ (G) dᵖ (H) γ d p (G ⊠ H) ≤ γ d p (G) γ d p (H). By proving that ₃^p (Pₘ Pₙ) = m2d+1 n2d+1 γ d p (P m ⊠ P n) = ⌈ m 2 d + 1 ⌉ ⌈ n 2 d + 1 ⌉, and that if ₃^p (Cₙ) γ d p (C n) ∞, then ₃^p (Pₘ Cₙ) = m2d+1 n2d+1 γ<
Bujtás et al. (Thu,) studied this question.