On Italian domination number of unary operations of special graphs

Abstract

For a graph G = (V, E), an Italian dominating function (IDF) f : V → {0, 1, 2} has the property that for every vertex v ∈ V with f(v) = 0, either v is adjacent to a vertex assigned 2 under f, or v is adjacent to at least two vertices assigned 1 under f. The weight of an Italian dominating function is the Pv∈V f(v), and the minimum weight of a Italian dominating function f is the Italian domination number. This study illustrates the Italian domination number of graphs that are generated when various unary operations are applied to standard graph classes.