Abstract
Augmented k-ary n-cube is 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 graph G, an edge-cut (vertex-cut) S is called a restricted edge-cut (restricted vertex-cut) if G–S contains no isolated vertices. The restricted edge-connectivity (restricted connectivity) of G, denoted by (), is the minimum cardinality over all restricted edge-cuts (vertex-cuts) of G. In this paper, we completely determine the restricted (edge-)connectivity of . Precisely, for ; for , for , for and , but does not have restricted vertex-cut.
Acknowledgments
The authors thank the anonymous referees for their helpful comments and suggestions.
Disclosure statement
No potential conflict of interest was reported by the authors.
ORCID
Ruizhi Lin http://orcid.org/0000-0002-4047-9891