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An algorithmic upper bound on the domination number $\gamma$ of graphs interms of the order $n$ and the minimum degree $\delta$ is proved. It isdemonstrated that the bound improves best previous bounds for any $5\le \delta\le 50$. In particular, for $\delta=5$, Xing et al.\ proved in 2006 that$\gamma \le 5n/14 < 0.3572 n$. This bound is improved to $0.3440 n$. For$\delta=6$, Clark et al.\ in 1998 established $\gamma <0.3377 n$, while Bir\'oet al. recently improved it to $\gamma <0.3340 n$. Here the bound is furtherimproved to $\gamma < 0.3159 n$. For $\delta=7$, the best earlier bound $0.3088 n$ is improved to $\gamma < 0.2927 n$.

Improved upper bounds on the domination number of graphs with minimum degree at least five