The orbits of Möbius cubes.
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| Title: | The orbits of Möbius cubes. |
|---|---|
| Authors: | Liu, Jia-Jie1 (AUTHOR) jjliu@mail.shu.edu.tw |
| Source: | Discrete Applied Mathematics. Aug2026, Vol. 389, p13-25. 13p. |
| Subjects: | Hypercubes, Graph theory, Computer network architectures |
| Abstract: | The M ö bius cube M Q n , a notable variant of the hypercube, is an interconnection network valued for its superior communication efficiency and low diameter. This paper investigates the network's structural homogeneity using the concept of graph orbits. The orbit number O r b (G) , which represents the number of distinct orbits that partition a graph's vertex set, provides a definitive measure of symmetry; O r b (G) = 1 signifies ideal structural equivalence (vertex-transitivity), as exemplified by the classic hypercube Q n. We demonstrate that while O r b (M Q n) = 1 for n ≤ 3 , this symmetry is lost in higher dimensions. Specifically, we prove that O r b (M Q 4) = 2 and O r b (M Q n) = 2 n − 2 for all n ≥ 5. This rapid growth in the orbit number demonstrates a critical lack of homogeneity for large n , highlighting a fundamental trade-off that severely complicates the SDN control plane and efficient load balancing. [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.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 193658957 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: The orbits of Möbius cubes. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Liu%2C+Jia-Jie%22">Liu, Jia-Jie</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> jjliu@mail.shu.edu.tw</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Discrete+Applied+Mathematics%22">Discrete Applied Mathematics</searchLink>. Aug2026, Vol. 389, p13-25. 13p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Hypercubes%22">Hypercubes</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> – Name: Abstract Label: Abstract Group: Ab Data: The M ö bius cube M Q n , a notable variant of the hypercube, is an interconnection network valued for its superior communication efficiency and low diameter. This paper investigates the network's structural homogeneity using the concept of graph orbits. The orbit number O r b (G) , which represents the number of distinct orbits that partition a graph's vertex set, provides a definitive measure of symmetry; O r b (G) = 1 signifies ideal structural equivalence (vertex-transitivity), as exemplified by the classic hypercube Q n. We demonstrate that while O r b (M Q n) = 1 for n ≤ 3 , this symmetry is lost in higher dimensions. Specifically, we prove that O r b (M Q 4) = 2 and O r b (M Q n) = 2 n − 2 for all n ≥ 5. This rapid growth in the orbit number demonstrates a critical lack of homogeneity for large n , highlighting a fundamental trade-off that severely complicates the SDN control plane and efficient load balancing. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab 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: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.dam.2026.03.022 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 13 StartPage: 13 Subjects: – SubjectFull: Hypercubes Type: general – SubjectFull: Graph theory Type: general – SubjectFull: Computer network architectures Type: general Titles: – TitleFull: The orbits of Möbius cubes. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Liu, Jia-Jie IsPartOfRelationships: – BibEntity: Dates: – D: 15 M: 08 Text: Aug2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 0166218X Numbering: – Type: volume Value: 389 Titles: – TitleFull: Discrete Applied Mathematics Type: main |
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