The Enumeration of Trees by Height and Diameter

The enumeration of trees which was begun by Harary and Prins, is simplified and elaborated in the interest of obtaining reliable numerical results. Height is a characteristic of a rooted tree, the length in lines of the longest path from the root, while the diameter of a (free) tree is the length of the longest path joining two endpoints. The most general enumerations given are for the case where a fixed number of the points of the trees are labeled with distinct labels, which puts in one setting the classical contrast of all points alike and all points unlike. The numerical tables given extend to trees with 20 points, all alike, and to trees with 10 points, all unlike.