On Relation between two Classes of Extremal Treeswith Prescribed Degree Sequence

A nonpendant vertex of a graph is called a support vertex if it is adjacent to any leaf. This paper examines how two classes of extremal trees among all trees with a prescribed degree sequence can relate to each other: the class of trees minimizing the number of support vertices and the class of trees minimizing the domination number. Two specially defined values play important role here: the Slater number, proposed by Slater as a lower bound on domination number, and the lower bound on the number of the support vertices of a tree proposed by Kurnosov. In the paper, the problem of comparing the classes is completely solved in the case where the maximum of two values is the latter.