Ascending Domination decomposition of graphs

In this paper, we combine decomposition and domination and introduce the concept Ascending Domination Decomposition ($ADD$) of a graph $G$. An $ADD$ of a graph $G$ is a collection $psi={G_{1},G_{2},ldots,G_{n}}$ of subgraphs of $G$ such that, each $G_{i}$ is connected, every edge of $G$ is in exactly one $G_{i}$ and $gamma(G_{i})=i$, $1leqileq n$. In this paper, we prove $K_n$,$W_n$ and $K_{1,n}$ admit $ADD$. We also establish the characterization for the path and cycle that they should admit $ADD$. We also prove that the corona of path, cycle and star admit $ADD$.