Azarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21286220211201Line completion number of grid graph Pn × Pm2993131416510.22049/cco.2021.26884.1156ENJoseph VargheseKureetharaChrist University0000-0001-5030-3948MerinSebastianChrist UniversityJournal Article20200719The 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 graph of index $r$, $L_r(G)$, has as its vertices the sets of $r$-edges of $G$, with two adjacent if there is an edge in one set adjacent to an edge in the other set. The line completion number $lc(G)$ of a graph $G$ is the least positive integer $r$ for which $L_r(G)$ is a complete graph. In this paper, we find the line completion number of grid graph $P_n times P_m$ for various cases of $n$ and $m$.http://comb-opt.azaruniv.ac.ir/article_14165_3168ef556251b68f7f57b9cb0c2c7e96.pdf