Diameter, short paths and superconnectivity in digraphs Original Research Article

A connected digraph is said to be superconnected if it is maximally connected and every minimum disconnecting set F consists of the vertices adjacent to or from a given vertex not belonging to F. Let image be the minimum degree of the digraph and image be a positive integer such that image when image, or image for image. We prove that G is maximally connected or has a good superconnectivity if the diameter image and image, where image is a generalization of the semigirth image introduced by Fàbrega and Fiol (J. Graph Theory 13(6) (1989) 657). We also show that G is maximally connected if image and image. In the edge case, it is enough that image. Finally, the obtained results are applied to the iterated line digraphs.