Using a progressive withdrawal procedure to study superconnectivity in digraphs

A maximally connected digraph is said to be superconnected if every minimum disconnecting set F of vertices is trivial, i.e., it consists of the vertices adjacent to or from a given vertex not belonging to F . This work is devoted to presenting a sufficient condition — in terms of the so called parameter ` — on the diameter, in order to guarantee that the digraph is superconnected, giving also a lower bound for the superconnectivity parameter κ1 when nontrivial disconnecting sets exist. This result has been achieved with the help of a ‘progressive withdrawal procedure’ that establishes how far away a vertex can be to or from a given set of vertices. An analogous result is presented in terms of edges, assuring edge-superconnectivity and giving a lower bound for the parameter λ1.