| Abstrakt: |
AbstractAn Italian dominating function (IDF) of a graph G is a function f: V(G) → {0, 1, 2} satisfying the condition that for every v∈ Vwith f(v) = 0, Σu∈N(v)f(u) ≥ 2. The weight of an IDF on Gis the sum f(V) = Σv∈Vf(v) and the Italian domination number, γI(G), is the minimum weight of an IDF. An IDF is a perfect Italian dominating function (PID) on G, if for every vertex v∈ V(G) with f(v) = 0 the total weight assigned by fto the neighbours of vis exactly 2, i.e., all the neighbours of uare assigned the weight 0 by fexcept for exactly one vertex vfor which f(v) = 2 or for exactly two vertices vand wfor which f(v) = f(w) = 1. The weight of a PID-function is f(V) = Σu∈V(G)f(u). The perfect Italian domination number of G, denoted by , 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 Sierpiński graphs. |
