论文标题
关于森林中的最低主导套装和总占主导地位的数量
On the number of minimum dominating sets and total dominating sets in forests
论文作者
论文摘要
我们表明，具有统治数量$γ$的森林的最大占主导地位数量最多是$ \ sqrt {5}^γ$，并为每棵树的$γ$构造，具有支配数字$γ$，其具有$ \ \ frac {2} {5} {5} \ sqrt {5} \ sqrt {5} \ sqrt {5}^γ$ min的最低量。此外，我们反驳了Henning，Mohr和Rautenbach在森林中最低占主导地位的最低统治地位数量的猜想。
We show that the maximum number of minimum dominating sets of a forest with domination number $γ$ is at most $\sqrt{5}^γ$ and construct for each $γ$ a tree with domination number $γ$ that has more than $\frac{2}{5}\sqrt{5}^γ$ minimum dominating sets. Furthermore, we disprove a conjecture about the number of minimum total dominating sets in forests by Henning, Mohr and Rautenbach.
