## Abstract

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 <formula><tex>$M$</tex></formula> of at most <formula><tex>$3n-7$</tex></formula> processors is deleted from an <formula><tex>$n$</tex></formula>-star graph, the surviving graph has a large component of size greater or equal to <formula><tex>$n!-|M|-3$</tex></formula>. We then prove that when a set <formula><tex>$M$</tex></formula> of at most <formula><tex>$4n-9$</tex></formula> processors is deleted from an <formula><tex>$n$</tex></formula>-star graph, the surviving graph has a large component of size greater or equal to <formula><tex>$n!-|M|-5$</tex></formula>. Finally, we also calculate the <formula><tex>$r$</tex></formula>-component connectivity of the <formula><tex>$n$</tex></formula>-star graph for <formula><tex>$2\leq r\leq 5$</tex></formula>.

Original language | English |
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Journal | IEEE Transactions on Reliability |

DOIs | |

Publication status | Accepted/In press - 2020 |

## All Science Journal Classification (ASJC) codes

- Safety, Risk, Reliability and Quality
- Electrical and Electronic Engineering