exact double domination in the generalized sierpiński graphs

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 sierpi´nski 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 sierpi´nski graphs s(pn, t), s(cn, t), s(k1,n, t) and s(kn, t).