Maximum number of edges in a critically k-connected graph

A k-connected graph G is said to be critically k-connected if G - v is not k-connected for any v is an element of V(G). We show that if n, k are integers with k greater than or equal to 4 and n greater than or equal to k + 2, and G is a critically k-connected graph of order n, then \E(G)\ less than or equal to n(n - 1)/2 - p(n - k) + [p(2)/2], where p = (n/k) + 1 if n/k is an odd integer and p = [n/k] otherwise. We also characterize extremal graphs. (C) 2002 Elsevier Science B.V. All rights reserved.