Some results on domination number of the graph defined by two levels of the n-cube

Let $\left(\genfrac{}{}{0px}{}{[n]}{k}\right)$ and $\left(\genfrac{}{}{0px}{}{[n]}{l}\right)$ $(k>l)$ where $[n] = {1,2,3,…,n}$denotethefamilyofall$k$-elementsubsetsand$l$-element subsets of $[n]$ respectively. Define a bipartite graph $G_{k,l} = ({[n] \choose k},{[n] \choose l},E)$suchthattwovertices$S, \epsilon ,{[n] \choose k} $and$T, \epsilon ,{[n] \choose l} $areadjacentifandonlyif$T \subset S$. In this paper, we give an upper bound for the domination number of graph $G_{k,2}$ for $k>\lceil \frac{n}{2}\rceil$ and exact value for $k=n-1$.