Impact of Vertex Addition on Italian Domination Number

An Italian dominating function (IDF), of a graph G is a function $f: V(G) \rightarrow \{0,1,2\}$ satisfying the condition that for every $v\in V(G)$ with $f(v) = 0, \sum_{ u\in N(v)} f(u) \geq 2.$ The weight of an IDF on $G$ is the sum $f(V)= \sum_{v\in V(G)}f(v)$ and Italian domination number, $\gamma_I(G)$ is the minimum weight of an IDF. In this paper, we study the impact of corona operator and addition of twins on Italian domination number.