Fault-tolerant analysis of augmented cubes

Abstract

The augmented cube $A{Q}_n$, 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 $(n\ge 4)$. This paper determines that the 2-extra connectivity of $A{Q}_n$ is $6n-17$ for $n\ge 9$ and the 2-extra edge-connectivity is $6n-9$ for $n\ge 4$. That is, for $n\ge 9$ (respectively, $n\ge 4$), at least $6n-17$ vertices (respectively, $6n-9$ edges) of $A{Q}_n$ 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.