A subset D of vertices of a simple graph G is an exact double dominating set if each vertex v of G is dominated by exactly two vertices of D, i. e. |NGv D|=2, in which NGv is the closed neighborhood of v in G. The generalized Sierpiński graph S (G, t) is a fractal-like graph that uses G as a building block and can be constructed recursively in t steps from the base graph G. In this paper we study and determine the existence of exact double dominating sets in generalized Sierpiński graphs S (Pₙ, t), S (Cₙ, t), S (K₁, ₍, t) and S (Kₙ, t) .
Khatibi et al. (Wed,) studied this question.