On the superconnectivity of generalized p-cycles

A generalized p-cycle is a digraph whose set of vertices can be partitioned into p parts that are cyclically ordered in such a way that the vertices in one part are adjacent only to vertices in the next part. Any digraph can be shown as a p-cycle with p = 1, and bipartite digraphs are generalized p-cycles with p = 2. A maximally connected digraph is said to be superconnected if every disconnecting set of δ vertices or edges is trivial, where δ stands for the minimum degree. In this work we study the problem of disconnecting p-cycles by removing nontrivial subsets of vertices or edges. To be more precise, after obtaining optimal lower bounds for the parameters κ1, λ1, that measure the superconnectivities, we present sufficient conditions for a p-cycle to be superconnected, and also sufficient conditions to guarantee optimum values of superconnectivities of a p-cycle. Finally, we apply our results to compute the superconnectivities of the family of De Bruijn generalized cycles.