7Augmented k-ary n-cube AQ n,k is proposed as a new interconnection network 8 model by Xiang and Steward [Augmented k-ary n-cubes, Information Sciences 182 9 (2011) 239-256]. For a connected graph G, an edge-cut (vertex-cut) S is called 10 a restricted edge-cut (restricted vertex-cut) if G − S contains no isolated vertices.11The restricted edge-connectivity (restricted connectivity) of G, denoted by λ (G) 12 (κ (G)), is the minimum cardinality over all restricted edge-cuts (vertex-cuts) of G.
13In this paper, we completely determine the restricted (edge-)connectivity of AQ n,k . 14 Precisely, λ (AQ n,k ) = 8n−6 for n 2; κ (AQ 2,k ) = 8 for k 4, κ (AQ n,3 ) = 8n−11 15 for n 3, κ (AQ n,k ) = 8n − 10 for n 3 and k 4, but AQ 2,3 does not have 16 restricted vertex-cut.
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