An asymptotic formula for the number of graphs having small diameter Original Research Article

In this paper it is shown that for every fixed k ⩾ 3, G(w, d = k) = 2(2n) (6·2−k + o(1))n, where G(n; d = k) denotes the number of graphs of order n and diameter equal to k. It is also proved that for every fixed k ⩾ 2, limn→∞ G(n; d = k)/G(n; d = k + 1) = limn→∞ G(n; d = n − k)/G(n; d = n − k + 1) = ∞ hold.