论文标题
线完整的网格图$ p_n \ times p_m $
Line Completion Number of Grid Graph $P_n \times P_m$
论文作者
论文摘要
超级线图的概念是由Bagga，Beineke和Varma在1995年引入的。给定具有至少$ r $边缘的图形，索引$ r $，$ l_r（g）$的超级线图作为$ r $ g $的$ r $边缘的套件，如果在另一组相邻的一组中，则有两个相邻。图$ g $的线完成号$ lc（g）$是$ l_r（g）$的最小正整数$ r $。在本文中，我们发现各种$ n $和$ m $的网格图$ p_n \ times p_m $的线完成数。
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 $m$.
