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Strong Reliability of Star Graphs Interconnection Networks.

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Title: Strong Reliability of Star Graphs Interconnection Networks.
Authors: Lin, Limei1 (AUTHOR) putianlinlimei@163.com, Huang, Yanze2 (AUTHOR) yzhuang@fjut.edu.cn, Hsieh, Sun-Yuan3 (AUTHOR) hsiehsy@mail.ncku.edu.tw, Xu, Li1 (AUTHOR) xuli@fjnu.edu.cn
Source: IEEE Transactions on Reliability. Sep2022, Vol. 71 Issue 3, p1241-1254. 14p.
Subjects: Distributed computing, Fault tolerance (Engineering), Parallel programming, Hypercubes
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 $M$ 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 $2\leq r\leq 5$. [ABSTRACT FROM AUTHOR]
Copyright of IEEE Transactions on Reliability is the property of IEEE and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: 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 $2\leq r\leq 5$. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of IEEE Transactions on Reliability is the property of IEEE and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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              M: 09
              Text: Sep2022
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