“…From the practical point of view we need to study the stability of the radius and the diameter of a graph G, especially when an arbitrary edge or vertex is removed from G. This operation can represent a single failure of communication line or any communication center (processor, etc.). The papers [1], [3], [5], [13] examine several properties of graphs in which radii do not change under these two conditions, and moreover, when an arbitrary edge is added to the graph G. These graphs are defined as follows: Definition 1.1. A graph G is:…”