Computation of the center and diameter of outerplanar graphs

The center of a graph is the set of vertices with minimum eccentricity. An outerplanar graph is a planar segmentation of a polygon. We define a notion of edge eccentricities for the edges of an outerplanar graph. We present an algorithm which efficiently computes these edge eccentricities. Knowledge of the edge eccentricities allows subsequent linear time computation of the center and diameter of outerplanar graphs. The computation of edge eccentricities is shown to require linear time for certain subclasses of outerplanar graphs.