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A concentration phenomenon for h-extra edge-connectivity reliability analysis of enhanced hypercubes Qn,2 with exponentially many faulty links.

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Title: A concentration phenomenon for h-extra edge-connectivity reliability analysis of enhanced hypercubes Qn,2 with exponentially many faulty links.
Authors: Sun, Yali1 ylisun@163.com, Zhang, Mingzu1 mzuzhang@163.com, Feng, Xing2 fengxingfm@163.com, Yang, Xing3 xyang4@monroecc.edu
Source: Fundamenta Informaticae. 2025, Vol. 194 Issue 1, p1-21. 20p.
Subjects: Hypercubes, Graph connectivity, Engineering reliability theory, Computer network reliability, Multiprocessors, Multistage interconnection networks, Reliability in engineering
Abstract: Reliability assessment of interconnection networks is critical to the design and maintenance of multiprocessor systems. The (n, k)-enhanced hypercube Qn,k, as a variation of the hypercube Qn, was proposed by Tzeng and Wei in 1991. As an extension of traditional edgeconnectivity, h-extra edge-connectivity of a connected graph G, λh(G), is an essential parameter for evaluating the reliability of interconnection networks. This article intends to study the h-extra edge-connectivity of the (n, 2)-enhanced hypercube Qn,2. Suppose that the link malfunction of an interconnection network Qn,2 does not isolate any subnetwork with no more than h - 1 processors, the minimum number of these possible faulty links concentrates on a constant 2n-1 for each integer ... That is, for about 77.083% of values where h ≤ 2n-1, the corresponding h-extra edge-connectivity of Qn,2, λh(Qn,2), presents a concentration phenomenon. Moreover, the lower and upper bounds of h mentioned above are both tight. [ABSTRACT FROM AUTHOR]
Copyright of Fundamenta Informaticae is the property of Polskie Towarzystwo Matematyczne 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: A concentration phenomenon for h-extra edge-connectivity reliability analysis of enhanced hypercubes Qn,2 with exponentially many faulty links.
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  Data: <searchLink fieldCode="AR" term="%22Sun%2C+Yali%22">Sun, Yali</searchLink><relatesTo>1</relatesTo><i> ylisun@163.com</i><br /><searchLink fieldCode="AR" term="%22Zhang%2C+Mingzu%22">Zhang, Mingzu</searchLink><relatesTo>1</relatesTo><i> mzuzhang@163.com</i><br /><searchLink fieldCode="AR" term="%22Feng%2C+Xing%22">Feng, Xing</searchLink><relatesTo>2</relatesTo><i> fengxingfm@163.com</i><br /><searchLink fieldCode="AR" term="%22Yang%2C+Xing%22">Yang, Xing</searchLink><relatesTo>3</relatesTo><i> xyang4@monroecc.edu</i>
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  Data: <searchLink fieldCode="JN" term="%22Fundamenta+Informaticae%22">Fundamenta Informaticae</searchLink>. 2025, Vol. 194 Issue 1, p1-21. 20p.
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  Data: <searchLink fieldCode="DE" term="%22Hypercubes%22">Hypercubes</searchLink><br /><searchLink fieldCode="DE" term="%22Graph+connectivity%22">Graph connectivity</searchLink><br /><searchLink fieldCode="DE" term="%22Engineering+reliability+theory%22">Engineering reliability theory</searchLink><br /><searchLink fieldCode="DE" term="%22Computer+network+reliability%22">Computer network reliability</searchLink><br /><searchLink fieldCode="DE" term="%22Multiprocessors%22">Multiprocessors</searchLink><br /><searchLink fieldCode="DE" term="%22Multistage+interconnection+networks%22">Multistage interconnection networks</searchLink><br /><searchLink fieldCode="DE" term="%22Reliability+in+engineering%22">Reliability in engineering</searchLink>
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  Data: Reliability assessment of interconnection networks is critical to the design and maintenance of multiprocessor systems. The (n, k)-enhanced hypercube Qn,k, as a variation of the hypercube Qn, was proposed by Tzeng and Wei in 1991. As an extension of traditional edgeconnectivity, h-extra edge-connectivity of a connected graph G, λh(G), is an essential parameter for evaluating the reliability of interconnection networks. This article intends to study the h-extra edge-connectivity of the (n, 2)-enhanced hypercube Qn,2. Suppose that the link malfunction of an interconnection network Qn,2 does not isolate any subnetwork with no more than h - 1 processors, the minimum number of these possible faulty links concentrates on a constant 2n-1 for each integer ... That is, for about 77.083% of values where h ≤ 2n-1, the corresponding h-extra edge-connectivity of Qn,2, λh(Qn,2), presents a concentration phenomenon. Moreover, the lower and upper bounds of h mentioned above are both tight. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Fundamenta Informaticae is the property of Polskie Towarzystwo Matematyczne 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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        Value: 10.46298/fi.13487
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        Text: English
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        PageCount: 20
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        Type: general
      – SubjectFull: Graph connectivity
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      – SubjectFull: Engineering reliability theory
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      – SubjectFull: Computer network reliability
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      – SubjectFull: Multiprocessors
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      – SubjectFull: Multistage interconnection networks
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      – SubjectFull: Reliability in engineering
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      – TitleFull: A concentration phenomenon for h-extra edge-connectivity reliability analysis of enhanced hypercubes Qn,2 with exponentially many faulty links.
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            NameFull: Sun, Yali
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            NameFull: Zhang, Mingzu
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              M: 07
              Text: 2025
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              Y: 2025
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