Strong Reliability of Star Graphs Interconnection Networks

For interconnection network losing processors, it is considerable to calculate the number of vertices in the maximal component in the surviving network. Moreover, the component connectivity is a significant indicator for reliability of a network in the presence of failing processors. In this article, we first prove that when a set $M$ of at most $3n-7$ processors is deleted from an $n$ -star graph, the surviving graph has a large component of size greater or equal to $n!-|M|-3$ . We then prove that when a set $M$ of at most $4n-9$ processors is deleted from an $n$ -star graph, the surviving graph has a large component of size greater or equal to $n!-|M|-5$ . Finally, we also calculate the $r$ -component connectivity of the $n$ -star graph for $2\leq r\leq 5$ .