We revisit the problem of determining the independent domination number in hypercubes for which the known upper bound is still not tight for general dimensions. We present here a constructive method to build an independent dominating set $S_n$ for the $n$-dimensional hypercube $Q_n$, where $n=2p+1$, $p$ being a positive integer $\ge 1$, provided an independent dominating set $S_p$ for the $p$-dimensional hypercube $Q_p$, is known. The procedure also computes the minimum independent dominating set for all $n=2^k-1$, $k>1$. Finally, we establish that the independent domination number $\alpha_n\leq 3 \times 2^{n-k-2}$ for $7\times 2^{k-2}-1\leq n<2^{k+1}-1$, $k>1$. This is an improved upper bound for this range as compared to earlier work.

翻译：我们重新审视了确定超立方体中独立支配号的问题,已知的超立方体的上限在一般维度方面仍然不紧紧。我们在此提出了一个建设性的方法,用于为美元-维超立方美元建立一个独立的主宰设为S_n美元,其中美元=2p+1美元,美元为正整数1美元,但需知道为美元-维超立方美元设定独立的控制设为S_p美元。该程序还计算了所有美元=2 ⁇ k-1美元($k>1美元)的最低独立控制设为S_n美元。最后,我们确定独立控制设为$\alpha_n\leq 3 time 2 ⁇ n-k2}美元-k2美元(美元)美元,为正数 2 ⁇ k-2美元=leq n\leq n@leq n<2 ⁇ k+1美元($)美元),这是与先前工作相比,这一范围上限值的改进。