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 -