  In this paper arithmetic progressions on the integers and the integers modulo
n are extended to graphs. This allows for the definition of the anti-van der
Waerden number of a graph. Much of the focus of this paper is on 3-term
arithmetic progressions for which general bounds are obtained based on the
radius and diameter of a graph. The general bounds are improved for trees and
Cartesian products and exact values are determined for some classes of graphs.
Larger k-term arithmetic progressions are considered and a connection between
the Ramsey number of paths and the anti-van der Waerden number of graphs is
established.
