Let G be a graph and S be a subset of vertices of G. With I[S] we denote the set of all vertices on some geodesic (shortest path) between two vertices of S. A contour vertex of a graph is one whose eccentricity is at least as big as all its neighbors' eccentricities. Let C be the set of contour vertices of a graph. We provide the first example of a graph where I[I[C]] do not coincide with the vertex set of the graph.
Mezzini, M. (2016). On the geodetic iteration number of the contour of a graph. DISCRETE APPLIED MATHEMATICS, 206, 211-214 [10.1016/j.dam.2016.02.012].