Optimally restricted edge connected elementary Harary graphs

An edge subset F of a connected graph G=(V,E) is a k-restricted edge cut if G-F is disconnected, and every component of G-F has at least k vertices. The k-restricted edge connectivity of G, denoted by @l"k(G), is the cardinality of a minimum k-restricted edge cut. By the current studies on @l"k, it can be seen that the larger @l"k is, the more reliable the graph is. Hence one expects @l"k to be as large as possible. A possible upper bound for @l"k is @x"k defined as @x"k(G)=min{@w(S):[email protected]? [email protected]?V(G),|S|=k and G[S] is connected }, where @w(S) is the number of edges with one end in S and the other end in V(G)@?S, and G[S] is the subgraph of G induced by S. A graph G is called @l"k-optimal if @l"k(G)[email protected]"k(G). A natural question is whether there exists a graph G which is @l"k-optimal for any [email protected]?|V(G)|/2. In this paper, we show that except for two cases, the elementary Harary graph has this property.