Sharp bounds on the diameter of a graph

Abstract Let D n.m , be the diameter of a connected undirected graph on n ≥2 vertices and n - 1 ≤ m ≤ s(n) edges, where s(n) = n(n — l)/2. Then D n.s(n) = 1, and for m s(n) it is shown that The bounds on D n.m , are sharp.