Fault-tolerant analysis of augmented cubes

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 (2n − 1)-regular (2n − 1)-connected graph (n ≥ 4). This paper determines that the 2-extra connectivity of AQ n is 6n − 17 for n ≥ 9 and the 2-extra edge-connectivity is 6n − 9 for n ≥ 4. That is, for n ≥ 9 (respectively, n ≥ 4), at least 6n−17 vertices (respectively, 6n − 9 edges) of AQ n have to be removed to get a disconnected graph that contains no isolated vertices and isolated edges. 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.