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 not equal 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. (C) 2007 Elsevier B.V. All rights reserved.