Extremal connectivity and vulnerability in graphs

If a practical network is modelled as a graph in which the lines are perfect but the points may fail then a primary measure of vulnerability is the point connectivity of the graph and one possible secondary measure of vulnerability is the number of minimum point disconnecting sets. The graph shold have the maximum possible point connectivity and the minimum number of point disconnecting sets. A lower bound for the number of minimum point disconnecting sets is derived by identifying points with identical adjacencies.