# Algebra & Combinatorics Seminar

"The Center Function on Ptolemaic Graphs"

Professor Robert Powers

Thursday November 8th at 10 am in NS 333

Let G = (V,E) be a finite connected graph. The _center function_ Cen on G takes as input any nonempty subset pi of V and outputs Cen(pi), the set of all vertices that minimize the maximum distance to pi. If G is a tree and a subset pi of V has at least two elements, then there exist distinct x and y in pi such that Cen(pi) = Cen(x, y). The previous fact, called the (EXP) property, may not hold if G is not a tree. The goal of my talk is to argue that the (EXP) property holds when G is a ptolemaic graph.

This project is in collaboration with Steve Seif and Martyn Mulder.