On the geodetic iteration number of the contour of a graph

Let GG be a graph and SS be a subset of vertices of GG. With I[S]I[S] we denote the set of all vertices on some geodesic (shortest path) between two vertices of SS. A contour vertex of a graph is one whose eccentricity is at least as big as all its neighbors’ eccentricities. Let CC be the set of contour vertices of a graph. We provide the first example of a graph where I[I[C]]I[I[C]] do not coincide with the vertex set of the graph.