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Fault tolerability analysis of hypercubes based on the [formula omitted]-cyclic fault pattern.

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Title: Fault tolerability analysis of hypercubes based on the [formula omitted]-cyclic fault pattern.
Authors: Tian, Ting1 (AUTHOR) tianting1201@163.com, Zhang, Shumin1,2,3 (AUTHOR) zhangshumin@qhnu.edu.cn, Zhu, Bo1 (AUTHOR) zhuboqh@163.com, Chang, Jou-Ming4 (AUTHOR) spade@ntub.edu.tw
Source: Discrete Applied Mathematics. Jun2026, Vol. 386, p293-305. 13p.
Subjects: Hypercubes, Graph connectivity, Graph theory, Computer network architectures, Fault tolerance (Engineering)
Abstract: The connectivity of a graph and its various generalizations have been extensively studied due to their significant impact on fault tolerance in interconnection networks. In this paper, we further elaborate on the concept of cyclic connectivity and propose a novel form of it. Given a connected graph G = (V (G) , E (G)) and an integer g ≥ 1 , a g -cyclic vertex cut of G is a vertex subset S ⊆ V (G) such that G − S is disconnected and there are at least g + 1 components containing cycles. The g -cyclic connectivity of G , denoted by κ c g (G) , is defined as the cardinality of a minimum g -cyclic vertex cut of G. Then, we derive an upper bound for the g -cyclic connectivity of the n -dimensional hypercube Q n. Specifically, κ c g (Q n) ≤ 4 g (n − 2) − 2 g (g + 1) + 4 for n ≥ 4 and 1 ≤ g ≤ n − 3. Moreover, we determine the exact g -cyclic connectivity of Q n as κ c g (Q n) = 4 g (n − 2) − 2 g (g + 1) + 4 for g ∈ { 1 , 2 , 3 } when n is sufficiently large. [ABSTRACT FROM AUTHOR]
Copyright of Discrete Applied Mathematics is the property of Elsevier B.V. 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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DbLabel: Engineering Source
An: 192967411
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  Data: Fault tolerability analysis of hypercubes based on the [formula omitted]-cyclic fault pattern.
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  Data: <searchLink fieldCode="AR" term="%22Tian%2C+Ting%22">Tian, Ting</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> tianting1201@163.com</i><br /><searchLink fieldCode="AR" term="%22Zhang%2C+Shumin%22">Zhang, Shumin</searchLink><relatesTo>1,2,3</relatesTo> (AUTHOR)<i> zhangshumin@qhnu.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Zhu%2C+Bo%22">Zhu, Bo</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> zhuboqh@163.com</i><br /><searchLink fieldCode="AR" term="%22Chang%2C+Jou-Ming%22">Chang, Jou-Ming</searchLink><relatesTo>4</relatesTo> (AUTHOR)<i> spade@ntub.edu.tw</i>
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  Data: <searchLink fieldCode="JN" term="%22Discrete+Applied+Mathematics%22">Discrete Applied Mathematics</searchLink>. Jun2026, Vol. 386, p293-305. 13p.
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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="%22Graph+theory%22">Graph theory</searchLink><br /><searchLink fieldCode="DE" term="%22Computer+network+architectures%22">Computer network architectures</searchLink><br /><searchLink fieldCode="DE" term="%22Fault+tolerance+%28Engineering%29%22">Fault tolerance (Engineering)</searchLink>
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  Data: The connectivity of a graph and its various generalizations have been extensively studied due to their significant impact on fault tolerance in interconnection networks. In this paper, we further elaborate on the concept of cyclic connectivity and propose a novel form of it. Given a connected graph G = (V (G) , E (G)) and an integer g ≥ 1 , a g -cyclic vertex cut of G is a vertex subset S ⊆ V (G) such that G − S is disconnected and there are at least g + 1 components containing cycles. The g -cyclic connectivity of G , denoted by κ c g (G) , is defined as the cardinality of a minimum g -cyclic vertex cut of G. Then, we derive an upper bound for the g -cyclic connectivity of the n -dimensional hypercube Q n. Specifically, κ c g (Q n) ≤ 4 g (n − 2) − 2 g (g + 1) + 4 for n ≥ 4 and 1 ≤ g ≤ n − 3. Moreover, we determine the exact g -cyclic connectivity of Q n as κ c g (Q n) = 4 g (n − 2) − 2 g (g + 1) + 4 for g ∈ { 1 , 2 , 3 } when n is sufficiently large. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Discrete Applied Mathematics is the property of Elsevier B.V. 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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RecordInfo BibRecord:
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      – Type: doi
        Value: 10.1016/j.dam.2026.02.013
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 13
        StartPage: 293
    Subjects:
      – SubjectFull: Hypercubes
        Type: general
      – SubjectFull: Graph connectivity
        Type: general
      – SubjectFull: Graph theory
        Type: general
      – SubjectFull: Computer network architectures
        Type: general
      – SubjectFull: Fault tolerance (Engineering)
        Type: general
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      – TitleFull: Fault tolerability analysis of hypercubes based on the [formula omitted]-cyclic fault pattern.
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            NameFull: Tian, Ting
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            NameFull: Zhang, Shumin
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            NameFull: Zhu, Bo
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            NameFull: Chang, Jou-Ming
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            – D: 15
              M: 06
              Text: Jun2026
              Type: published
              Y: 2026
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              Value: 386
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            – TitleFull: Discrete Applied Mathematics
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