Using a progressive withdrawal procedure to study superconnectivity in digraphs Original Research Article

A maximally connected digraph is said to be superconnected if every minimum disconnecting set F of vertices is trivial, that is, 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 on the diameter—in terms of a so called parameter ℓ1 (which is related with the number of shortest paths)—in order to guarantee that the digraph is superconnected. We give also a lower bound for the superconnectivity parameter κ1, defined as the minimum order of a nontrivial disconnecting set of vertices. 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.