## DIMACS TR: 2000-41

## 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:
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