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Line Completion Number of Grid Graph $P n \times P m$ by Kureethara, Joseph Varghese; Sebastian, Merin is a scholarly article available to read on EtoBox.

What is Line Completion Number of Grid Graph $P n \times P m$ about?

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 $m$.

Author

Kureethara, Joseph Varghese; Sebastian, Merin

Published

2020

Language

EN