Conditional connectivity of star graph networks under embedding restriction

The n-dimensional star graph Sn is one of the most attractive interconnection networks of large scale multiprocessor systems. The k-embedding-restricted (edge) connectivity (ηk(Sn)) ζk(Sn) of Sn is defined to be the cardinality of a minimum subset of (edges) nodes, if any, whose deletion disconnects Sn and each node of the remaining components lies in an undamaged k-dimensional substar Sk. In this paper, we investigate the k-embedding-restricted (edge) connectivity of Sn and determine the values of ηk(Sn) and ζk(Sn) for some k’s.