The center function on trees

When (X, d) is a finite metric space and pi = (x(1),...,x(k)) is an element of X-k, a central element for pi is an element x of X for which max{d(x, x (i)): i = 1,...,k} is minimum. The function that returns the set of all cen tral elements for any tuple pi is called the center function on X. In this article, the center function on finite trees is characterized. (C) 2001 Joh n Wiley & Sons, Inc.