Are there any results on connected graphs with large diameters and small clique numbers? I am particularly interested interested in the maximum number of edges on graph with $n$ vertices, minimum diameter $d$, and maximum clique number $r$, as well as what the extremal graphs look like.
Turan's construction for dense $K_r$-free graphs has very small diameter whereas graphs with large diameter and many edges appear to have large clique number. I would be very grateful for any references.