Changing and unchanging of the radius of a graph Original Research Article

Harary introduced the concept of changing and unchanging of a graphical invariant i, asking for characterizations of graphs G = (V, E) for which i(G − v), i(G − e) or i(G + e) either differ from i(G) or are equal to i(G) for all v set membership, variant V, e set membership, variant E, or e set membership, variant E, respectively, where image is the set of edges in the complement of G. This paper examines changing and unchanging properties of the radius of a graph, an important parameter in network design.