Graphs of maximum diameter

A simple undirected connected graph with minimum degree K is said to be K-restrained. Thus the class of K-restrained graphs includes all K-connected and K-edge-connected graphs, as well as all connected K-regular graphs. An upper bound on the diameter of three of these four classes of graphs is known: for K-restrained (hence for connected K-regular) and for K-connected. We complete the picture by determining an upper bound on the diameter of a …