The restricted edge-connectivity and restricted connectivity of augmented k -ary n -cubes.

Augmentedk-aryn-cubeis proposed as a new interconnection network model by Xiang and Steward [Augmented k-ary n-cubes, Inform. Sci. 181(1) (2011), pp. 239–256]. For a connected graphG, an edge-cut (vertex-cut)Sis called a restricted edge-cut (restricted vertex-cut) ifG–Scontains no isolated vertices. The restricted edge-connectivity (restricted connectivity) ofG, denoted by(), is the minimum cardinality over all restricted edge-cuts (vertex-cuts) ofG. In this paper, we completely determine the restricted (edge-)connectivity of. Precisely,for;for,for,forand, butdoes not have restricted vertex-cut. [ABSTRACT FROM AUTHOR]