## The Center Function on Trees

### Authors: F. R. McMorris, Fred S. Roberts and Chi Wang

ABSTRACT

When $(X, d)$ is a finite metric space and $\pi = (x_1 , \ldots, x_k ) \in X^k$, a central element for $\pi$ is an element $x$ of $X$ for which max$\{ d(x, x_i ): i = 1 ,\ldots ,k\}$ is minimum. The function that returns the set of all central elements for any tuple $\pi$ is called the center function on $X$. In this note, the center function on finite trees is characterized.

Paper Available at: ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2000/2000-41.ps.gz