The super connectivity of augmented cubes

The augmented cube AQ"n, proposed by Choudum and Sunitha [S.A. Choudum, V. Sunitha, Augmented cubes, Networks 40 (2) (2002) 71-84], is a (2n-1)-regular (2n-1)-connected graph (n 3). This paper determines that the super connectivity of AQ"n is 4n-8 for n>=6 and the super edge-connectivity is 4n-4 for n>=5. That is, for n>=6 (respectively, n>=5), at least 4n-8 vertices (respectively, 4n-4 edges) of AQ"n are removed to get a disconnected graph that contains no isolated vertices. When the augmented cube is used to model the topological structure of a large-scale parallel processing system, these results can provide more accurate measurements for reliability and fault tolerance of the system.

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