The line completion number of hypercubes
S. A. Tapadia, B. N. Waphare · AKCE International Journal of Graphs and Combinatorics · 2018
In 1992, Bagga, Beineke, and Varma introduced the concept of the super line graph of index r of a graph G, denoted by ℒr(G). The vertices of ℒr(G) are the r-subsets of E(G), and two vertices S and T are adjacent if there exist s∈S and t∈T such that s and t are adjacent edges in G. They also defined the line completion number lc(G) of graph G to be the minimum index r for which ℒr(G) is complete. They found the line completion number for certain classes of graphs. In this paper, we find the line completion number of hypercube Qn for every n.