Let $G=(V,E)$ be a simple graph. Let $H$ be the graph constructed from $G$ as follows: $V(H)=V(G)$, two points $u$ and $v$ are adjacent in $H$ if and only if $u$ and $v$ are adjacent and degree equitable in $G$. $H$ is called the adjacency inherent equitable graph of G or equitable associate of $G$ and is denoted by $e(G)$. This Paper aims at the study of a new concept called equitable associate graph of a graph. In this paper we show that there is relation between $e(G)$ and $e^-(G)$. Further results on the new parameter $e(G),e^-(G)$ and complexity of equitable dominating set are discussed.