A subset $D$ of $V$ is called an equitable dominating set if for every $v \in V-D $ there exists $a$ vertex $u n D$ such that $u v n E(G)$ and $eft| ẹg(u)-ẹg (v) \right| eq 1$, where $ẹg(u)$ denotes the degree of vertex $u$ and $ẹg(v)$ denotes the degree of vertex $v$. The minimum cardinality of such a dominating set is denoted by $\gamma^{e}$ and is called the equitable domination number of $G$. This Paper aims at the study of a new concept called degree equitable domination introduced by Prof. E. Sampathkumar. Minimal equitable dominating sets are characterized. The complexity of the new parameter namely equitable domination number is determined.