Superconnected digraphs and graphs with small conditional diameters

The conditional diameter D of a digraph G measures how far apart a pair of vertex sets V1 and V2 can be in such a way that the minimum out-degree and the minimum in-degree of the subdigraphs induced by V1 and V2, respectively, are at least . Thus, D0 is the standard diameter and D0 D1 . . . D, where is the minimum degree. We prove that if D 2 - 3, where is a parameter related to the shortest paths, then G is maximally connected, superconnected or has a good superconnectivity, depending only on whether is equal to /2 , ( - 1)/2 , ( - 1)/3 , respectively. In the edge case, it is enough that D 2 - 2. The results for graphs are obtained as a corollary of those for digraphs, because in the undirected case, = (g - 1)/2 , g being the girth. Key words. digraphs, connectivity, superconnectivity, fault-tolerance, diameter, girth. AMS subject classification. 05C40, 05C20 References

• Type: Journal
• Year: 2002
• Where: NETWORKS
• Authors: Camino Balbuena, Josep Fàbrega, Xavier Marcote, Ignacio M. Pelayo
• Keywords: Computer Networks, Conditional Diameter, Minimum In-degree, NETWORKS 2002, Vertex Sets