We find the set of all values of the domination number for a class of trees with some given vertex degrees that forms a segment of naturals. We prove that each intermediate value of the segment can be obtained by gradually changing the tree that minimizes the domination number and with the use of two special operations, so that the last tree maximizes the domination number.

中文翻译：

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具有给定度数序列的树中支配数的所有值的集合

我们找到了具有一定给定顶点度的一类树木的支配数的所有值的集合，这些顶点形成自然部分。我们证明，通过逐渐改变最小化支配数的树并使用两个特殊运算，可以获取段的每个中间值，从而使最后一棵树最大化支配数。