Consider all $k$-element subsets and $\ell$-element subsets $(k>\ell )$ of an $n$-element set as vertices of a bipartite graph. Two vertices are adjacent if the corresponding $\ell$-element set is a subset of the corresponding $k$-element set. Let $G_{k,\ell }$ denote this graph. The domination number of $G_{k,1}$ was exactly determined by Badakhshian, Katona and Tuza. A conjecture was also stated there on the asymptotic value ($n$ tending to infinity) of the domination number of $G_{k,2}$. Here we prove the conjecture, determining the asymptotic value of the domination number $\gamma \left(G_{k,2}\right)=\frac{k+3}{2(k-1)(k+1)}{n}^2+o\left(n^2\right)$.

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图的支配数由两个层次的 $ñ$-立方体，二

考虑所有 $ķ$-元素子集和 $\ell$元素子集 $（ķ>\ell ）$ 的 $ñ$元素设置为二部图的顶点。如果对应的两个顶点相邻$\ell$-element set是相应元素的子集 $ķ$-元素集。让$G_{ķ，\ell }$表示该图。支配数$G_{ķ，\mathrm{1个}}$由Badakhshian，Katona和Tuza完全确定。那里也有一个关于渐近值的猜想（$ñ$ 趋于无穷大） $G_{ķ，2}$。在这里我们证明了猜想，确定了控制数的渐近值$\gamma （G_{ķ，2}）=\frac{ķ+3}{2（ķ-\mathrm{1个}）（ķ+\mathrm{1个}）}{ñ}^2+Ø（{ñ}^2）$。