TY - JOUR ID - 14165 TI - Line completion number of grid graph Pn × Pm JO - Communications in Combinatorics and Optimization JA - CCO LA - en SN - 2538-2128 AU - Kureethara, Joseph Varghese AU - Sebastian, Merin AD - Christ University Y1 - 2021 PY - 2021 VL - 6 IS - 2 SP - 299 EP - 313 KW - Line graph KW - Super line graph KW - Grid graph KW - Line completion number DO - 10.22049/cco.2021.26884.1156 N2 - 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 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 $m$. UR - http://comb-opt.azaruniv.ac.ir/article_14165.html L1 - http://comb-opt.azaruniv.ac.ir/article_14165_3168ef556251b68f7f57b9cb0c2c7e96.pdf ER -