Abstract
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 ( 2 n − 1 ) -regular ( 2 n − 1 ) -connected graph ( n ≠ 3 ). This paper determines that the super connectivity of AQ n is 4 n − 8 for n ⩾ 6 and the super edge-connectivity is 4 n − 4 for n ⩾ 5 . That is, for n ⩾ 6 (respectively, n ⩾ 5 ), at least 4 n − 8 vertices (respectively, 4 n − 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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