Let M be a finite subset of vertices of a connected graph G and assume that every vertex v E M has a dominating radius r(v)E N U {0}. A complete subgraph C is an r-dominating clique of M if every vertex vEM is at distance at most r(v) from C. Even for r(v)~ 1 the problem whether or not a given graph has an r-dominating clique is NP-complete. Evidently, if M admits an r-dominating clique then d(u, v)   5 as an isometric subgraph.
['Victor Chepoi']
A note on r -dominating cliques