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The k-Regular Edge Connectivity of Three Types of Regular Graphs.

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Τίτλος: The k-Regular Edge Connectivity of Three Types of Regular Graphs.
Συγγραφείς: Wang, Li1 (AUTHOR) wanglimath@hpu.edu.cn, Lin, Liqing1 (AUTHOR) linliqing@home.hpu.edu.cn, Zhao, Yanxia1 (AUTHOR) zhaoyanxia001@126.com
Πηγή: International Journal of Foundations of Computer Science. Apr2026, Vol. 37 Issue 3, p413-427. 15p.
Θεματικοί όροι: *Fault tolerance (Engineering), Regular graphs, Graph connectivity, Graph theory
Περίληψη: Let G be a connected graph. The k-regular edge cut F of G is a subset of E (G) such that G − F is disconnected and each component is k-regular. The k-regular edge connectivity of G, denoted as λ k r (G) , is the minimum cardinality of a k-regular edge cut in G. It is a generalization of traditional connectivity, which has better fault tolerability. In this paper, we determine the k-regular edge connectivity of three categories of graphs, which are pancake graph P n , burnt pancake graph B P n and godan graph E A n . Moreover, λ k r (P n) = (n − k − 1) × n ! 2 for n ≥ 3 (1 ≤ k ≤ n − 2), λ k r (B P n) = (n − k) × 2 n − 1 × n ! for n ≥ 2 (1 ≤ k ≤ n − 1) and λ k r (E A n) = (n − k) × n ! 2 for n ≥ 3 (1 ≤ k ≤ n − 1) are shown. [ABSTRACT FROM AUTHOR]
Copyright of International Journal of Foundations of Computer Science is the property of World Scientific Publishing Company 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: The k-Regular Edge Connectivity of Three Types of Regular Graphs.
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  Data: <searchLink fieldCode="AR" term="%22Wang%2C+Li%22">Wang, Li</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> wanglimath@hpu.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Lin%2C+Liqing%22">Lin, Liqing</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> linliqing@home.hpu.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Zhao%2C+Yanxia%22">Zhao, Yanxia</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> zhaoyanxia001@126.com</i>
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  Data: <searchLink fieldCode="JN" term="%22International+Journal+of+Foundations+of+Computer+Science%22">International Journal of Foundations of Computer Science</searchLink>. Apr2026, Vol. 37 Issue 3, p413-427. 15p.
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  Data: *<searchLink fieldCode="DE" term="%22Fault+tolerance+%28Engineering%29%22">Fault tolerance (Engineering)</searchLink><br /><searchLink fieldCode="DE" term="%22Regular+graphs%22">Regular graphs</searchLink><br /><searchLink fieldCode="DE" term="%22Graph+connectivity%22">Graph connectivity</searchLink><br /><searchLink fieldCode="DE" term="%22Graph+theory%22">Graph theory</searchLink>
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  Data: Let G be a connected graph. The k-regular edge cut F of G is a subset of E (G) such that G − F is disconnected and each component is k-regular. The k-regular edge connectivity of G, denoted as λ k r (G) , is the minimum cardinality of a k-regular edge cut in G. It is a generalization of traditional connectivity, which has better fault tolerability. In this paper, we determine the k-regular edge connectivity of three categories of graphs, which are pancake graph P n , burnt pancake graph B P n and godan graph E A n . Moreover, λ k r (P n) = (n − k − 1) × n ! 2 for n ≥ 3 (1 ≤ k ≤ n − 2), λ k r (B P n) = (n − k) × 2 n − 1 × n ! for n ≥ 2 (1 ≤ k ≤ n − 1) and λ k r (E A n) = (n − k) × n ! 2 for n ≥ 3 (1 ≤ k ≤ n − 1) are shown. [ABSTRACT FROM AUTHOR]
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  Label:
  Group: Ab
  Data: <i>Copyright of International Journal of Foundations of Computer Science is the property of World Scientific Publishing Company 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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    Identifiers:
      – Type: doi
        Value: 10.1142/S0129054125500157
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 15
        StartPage: 413
    Subjects:
      – SubjectFull: Fault tolerance (Engineering)
        Type: general
      – SubjectFull: Regular graphs
        Type: general
      – SubjectFull: Graph connectivity
        Type: general
      – SubjectFull: Graph theory
        Type: general
    Titles:
      – TitleFull: The k-Regular Edge Connectivity of Three Types of Regular Graphs.
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            NameFull: Wang, Li
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            NameFull: Lin, Liqing
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            NameFull: Zhao, Yanxia
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            – D: 01
              M: 04
              Text: Apr2026
              Type: published
              Y: 2026
          Identifiers:
            – Type: issn-print
              Value: 01290541
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              Value: 37
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              Value: 3
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            – TitleFull: International Journal of Foundations of Computer Science
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