Show that the vertex of largest degree in Bk is the root. A rooted tree T is called an Sk-tree if it satisfies this recursive definition. It is an S0-tree if it has one vertex. For k > 0, T is an Sk-tree if it can be built from two Sk-1-trees by making the root of one the root of the Sk-tree and making the root of the other the child of the root of the first Sk-1-tree.