Cuts leaving components of given minimum order

First we give useful equivalences to λpq-connectivity and κpq-connectivity and characterize the classes of graphs which are κ12-connected and κ13-connected. Then we prove κ1p(G)⩽λpp(G) which generalizes Whitney's well-known inequality κ(G)⩽λ(G). Finally, we characterize the class of graphs for which κ12(G) is minimum, i.e. κ12(G)=κ(G) and the class of graphs for which κ12(G) is maximum, i.e. κ12(G)=|V(G)|-3 or κ12(G)=λ22(G).