Transfiguring Trees

Hermione has come home for the holidays after a grueling first year at Hogwarts. She then picks up a Muggle book on "Graph Theory" and starts reading about rooted K-ary trees: Trees that are rooted and in which each node has at most K children. Since Transfiguration is her favorite subject at Hogwarts, she excitedly starts inventing a spell to Transfigure some such trees into others. After a whil