Impact of Vertex Addition on Italian Domination Number

Abstract

An Italian dominating function (IDF), of a graph G is a function $f:V(G)\to \{0,1,2\}$ satisfying the condition that for every $v\in V(G)$ with $f(v)=0,{\sum }_{u\in N(v)}f(u)\ge 2.$ 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.