  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 $(n\ge 4)$. This paper determines that the 2-extra
connectivity of $AQ_n$ is $6n-17$ for $n\geq 9$ and the 2-extra
edge-connectivity is $6n-9$ for $n\geq 4$. That is, for $n\geq 9$
(respectively, $n\geq 4$), 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.
