Italian domination and perfect Italian domination on Sierpiński graphs

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