Determines the existence of exact double dominating sets in various generalized Sierpiński graphs, highlighting their unique properties.
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. |NG[v]∩ D|=2, in which NG[v] 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,n,t) and S(Kₙ,t).
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Khatibi et al. (2026) studied this question.
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