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The concept of super line graph was introduced in the year 1995 by Bagga,Beineke and Varma. Given a graph with at least $r$ edges, the super line graphof index $r$, $L_r(G)$, has as its vertices the sets of $r$ edges of $G$, withtwo adjacent if there is an edge in one set adjacent to an edge in the otherset. The line completion number $lc(G)$ of a graph $G$ is the least positiveinteger $r$ for which $L_r(G)$ is a complete graph. In this paper, we find theline completion number of grid graph $P_n \times P_m$ for various cases of $n$and $m$.

Line Completion Number of Grid Graph $P_n \times P_m$