An Italian dominating function (IDF) of a graph G is a function f : V(G) -> {0, 1, 2} satisfying the condition that for every v is an element of V with f(v) = 0, Sigma(u) (is an element of N(v)) f(u) >= 2. The weight of an IDF on G is the sum f(V) = Sigma(v) (is an element of V) f(v) and the Italian domination number, gamma(I) (G), is the minimum weight of an IDF. An IDF is a perfect Italian dominating function (PID) on G, if for every vertex v is an element of V(G) with f(v) = 0 the total weight assigned by f to the neighbours of v is exactly 2, i.e., all the neighbours of u are assigned the weight 0 by f except for exactly one vertex v for which f(v) = 2 or for exactly two vertices v and w for which f(v) = f(w) = 1. The weight of a PID-function is f(V) = Sigma(u) (is an element of V(G)) f(u). The perfect Italian domination number of G, denoted by gamma(p)(I)(G), is the minimum weight of a PID-function of G. In this paper, we obtain the Italian domination number and perfect Italian domination number of Sierpinski graphs.
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