In this work, first, we present sufficient conditions for a bipartite digraph to attain optimum values of a stronger measure of connectivity, the so-called superconnectivity. To be more precise, we study the problem of disconnecting a maximally connected bipartite (di)graph by removing nontrivial subsets of vertices or edges. Within this framework, both an upper-bound on the diameter and Chartrand type conditions to guarantee optimum superconnectivities are obtained. Secondly, we show that if the order or size of a bipartite (di)graph is small enough then its vertex connectivity or edge-connectivity attain their maximum values. For example, a bipartite digraph is maximally edge-connected if δ~+(x) + δ~-(y) ≥ [(n + 1)/2] for all pair of vertices x,y such that d(x,y) ≥ 4. This result improves some conditions given by Dankelmann and Volkmann in [12] for the undirected case.
展开▼
