Extremal Problems for the Bondy-Chvátal Closure of a Graph

Let f(n) denote the maximum diameter of all graphs of order n whose Bondy-Chvátal n-closure is complete. It is shown that 3.2 logn − 9 ≤ f(n) ≤ 8.3 logn + 16. Let h(n) denote the maximum ratio of the number of edges in the n-closure of a graph of order n to the number of edges in the graph. It is shown that h(n) < 4; this bound is sharp.