On Maximum Induced Matching Numbers of Special Grids

Abstract

A subset $M$ of the edge set of a graph $G$ is an induced matching of $G$ if given any two $e_1,e_2 \in M$, none of the vertices on $e_1$ is adjacent to any of the vertices on $e_2$. Suppose that $MIM_G$, a positive integer, is the largest possible size of $M$ in $G$, then, $M$ is the maximum induced matching, $MIM$, of $G$ and $MIM_G$ is the maximum induced matching number of $G$. We obtain some upper bounds for the maximum induced matching numbers of some specific grids.