Minimal k‐arc connected graphs

A graph is k‐arc‐connected if it is necessary to remove at least k arcs in order to disconnect the graph. This paper solves the problem of determining the least number of arcs required in a k‐arc‐connected graph on n nodes by describing constructions that produce such graphs having kn/2 arcs (for kn éven) or (kn+1) /2 arcs (for kn odd). These results have application to the practical problem of synthesizing minimum cost, “k‐reliable” communication networks.