In basic graph theory books, we learn that the radius (rad) and diameter (diam) satisfy $$rad(G) \leq diam(G) \leq 2 rad(G)$$ I have seen books talk about graphs for which $rad(G) = diam(G)$. These graphs are called self-centered graphs. But, I have never seen anything on graphs satisfying the other bound, $diam(G) = 2 rad(G)$. I have googled for papers on the topic many times and never come up with anything. Do any of you know of any such papers/books that might mention this?