On maximum induced matching numbers of special grids

A subset M of the edge set of a graph G is an induced matching of $G$ if given any two edges $e_{1}; e_{2} \in M$, none of the vertices on $e_{1}$ is adjacent to any of the vertices on $e_{2}$. Suppose that $Max(G)$, a positive integer, denotes the maximum size of $M$ in $G$, then, $M$ is the maximum induced matching of $G$ and $Max(G)$ is the maximum induced matching number of $G$. In this work, we obtain upper bounds for the maximum induced matching number of grid $G = G_{n,m}, n \geq 9; m \equiv 3 \mod 4; m \geq 7, and nm$ odd.