Induced $nK_{2}$ decomposition of infinite square grids and infinite hexagonal grids

The induced $nK_2$ decomposition of infinite square grids and hexagonal grids are described here. We use the multi-level distance edge labeling as an effective technique in the decomposition of square grids. If the edges are adjacent, then their color difference is at least $2$ and if they are separated by exactly a single edge, then their colors must be distinct. Only non-negative integers are used for labeling. The proposed partitioning technique per the edge labels to get the induced $nK_2$ decomposition of the ladder graph is the square grid and the hexagonal grid.