Proceedings of the 1990 ACM/IEEE conference on Supercomputing
Information Processing Letters
Vertex-symmetric digraphs with small diameter
Discrete Applied Mathematics
On the Day—Tripathi orientation of the star graphs: connectivity
Information Processing Letters
Uni-directional Alternating Group Graphs
COCOON '95 Proceedings of the First Annual International Conference on Computing and Combinatorics
Connectivity of vertex and edge transitive graphs
Discrete Applied Mathematics
Conditional connectivity of Cayley graphs generated by transposition trees
Information Processing Letters
Conditional connectivity of star graph networks under embedding restriction
Information Sciences: an International Journal
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Day and Tripathi [K. Day, A. Tripathi, Unidirectional star graphs, Inform. Process. Lett. 45 (1993) 123-129] proposed an assignment of directions on the star graphs and derived attractive properties for the resulting directed graphs: an important one is that they are strongly connected. In [E. Cheng, M.J. Lipman, On the Day-Tripathi orientation of the star graphs: Connectivity, Inform. Process. Lett. 73 (2000) 5-10] it is shown that the Day-Tripathi orientations are in fact maximally arc-connected when n is odd; when n is even, they can be augmented to maximally arc-connected digraphs by adding a minimum set of arcs. This gives strong evidence that the Day-Tripathi orientations are good orientations. In [E. Cheng, M.J. Lipman, Connectivity properties of unidirectional star graphs, Congr. Numer. 150 (2001) 33-42] it is shown that vertex-connectivity is maximal, and that if we delete as many vertices as the connectivity, we can create at most two strong connected components, at most one of which is not a singleton. In this paper we prove an asymptotically sharp upper bound for the number of vertices we can delete without creating two nonsingleton strong components, and we also give sharp upper bounds on the number of singletons that we might create.