# Line completion number of grid graph Pn × Pm

Document Type : Original paper

Authors

Christ University

Abstract

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 $m$.

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