On equi independent equitable dominating sets in graphs

The concept of equi independent equitable domination is the combination of two important concepts, namely independent domination and equitable domination. A subset $D$ of $V(G)$ is called an equitable dominating set if for every $v in V(G)-D$, there exists a vertex $u in D$ such that $uv in E(G)$ and $|deg(u)-deg(v)|leq 1$. A vertex subset $D$ is said to be equitable independent set if any two vertices of $D$ are either non adjacent or if adjacent then their degrees differ by atleast 2. An equitable dominating set $D$ is said to be an equi independent equitable dominating set if it is also equitable independent set. The equi independent equitable domination number $i^e$ is the minimum cardinality of an equi independent equitable dominating set.