Algebraic connectivity in normed spaces.
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| Title: | Algebraic connectivity in normed spaces. |
|---|---|
| Authors: | Cruickshank, James1 (AUTHOR) james.cruickshank@universityofgalway.ie, Dewar, Sean2 (AUTHOR) sean.dewar@bristol.ac.uk, Kitson, Derek1,3 (AUTHOR) derek.kitson@mic.ul.ie |
| Source: | Linear Algebra & its Applications. Jun2026, Vol. 739, p10-42. 33p. |
| Subjects: | Graph theory, Geometric rigidity, Graph connectivity, Metric spaces, Isomorphism (Mathematics) |
| Abstract: | The algebraic connectivity of a graph G in a finite dimensional real normed linear space X is a geometric counterpart to the Fiedler number of the graph and can be regarded as a measure of the rigidity of the graph in X. We analyse the behaviour of the algebraic connectivity of G in X with respect to graph decomposition, vertex deletion and isometric isomorphism, and provide a general bound expressed in terms of the geometry of X and the Fiedler number of the graph. Particular focus is given to the space ℓ ∞ d where we present explicit formulae and calculations as well as upper and lower bounds. As a key tool, we show that the monochrome subgraphs of a complete framework in ℓ ∞ d are odd-hole-free. Connections to redundant rigidity are also presented. [ABSTRACT FROM AUTHOR] |
| Copyright of Linear Algebra & its Applications 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: 192692798 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Algebraic connectivity in normed spaces. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Cruickshank%2C+James%22">Cruickshank, James</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> james.cruickshank@universityofgalway.ie</i><br /><searchLink fieldCode="AR" term="%22Dewar%2C+Sean%22">Dewar, Sean</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> sean.dewar@bristol.ac.uk</i><br /><searchLink fieldCode="AR" term="%22Kitson%2C+Derek%22">Kitson, Derek</searchLink><relatesTo>1,3</relatesTo> (AUTHOR)<i> derek.kitson@mic.ul.ie</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Linear+Algebra+%26+its+Applications%22">Linear Algebra & its Applications</searchLink>. Jun2026, Vol. 739, p10-42. 33p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Graph+theory%22">Graph theory</searchLink><br /><searchLink fieldCode="DE" term="%22Geometric+rigidity%22">Geometric rigidity</searchLink><br /><searchLink fieldCode="DE" term="%22Graph+connectivity%22">Graph connectivity</searchLink><br /><searchLink fieldCode="DE" term="%22Metric+spaces%22">Metric spaces</searchLink><br /><searchLink fieldCode="DE" term="%22Isomorphism+%28Mathematics%29%22">Isomorphism (Mathematics)</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: The algebraic connectivity of a graph G in a finite dimensional real normed linear space X is a geometric counterpart to the Fiedler number of the graph and can be regarded as a measure of the rigidity of the graph in X. We analyse the behaviour of the algebraic connectivity of G in X with respect to graph decomposition, vertex deletion and isometric isomorphism, and provide a general bound expressed in terms of the geometry of X and the Fiedler number of the graph. Particular focus is given to the space ℓ ∞ d where we present explicit formulae and calculations as well as upper and lower bounds. As a key tool, we show that the monochrome subgraphs of a complete framework in ℓ ∞ d are odd-hole-free. Connections to redundant rigidity are also presented. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Linear Algebra & its Applications 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.laa.2026.03.009 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 33 StartPage: 10 Subjects: – SubjectFull: Graph theory Type: general – SubjectFull: Geometric rigidity Type: general – SubjectFull: Graph connectivity Type: general – SubjectFull: Metric spaces Type: general – SubjectFull: Isomorphism (Mathematics) Type: general Titles: – TitleFull: Algebraic connectivity in normed spaces. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Cruickshank, James – PersonEntity: Name: NameFull: Dewar, Sean – PersonEntity: Name: NameFull: Kitson, Derek IsPartOfRelationships: – BibEntity: Dates: – D: 15 M: 06 Text: Jun2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 00243795 Numbering: – Type: volume Value: 739 Titles: – TitleFull: Linear Algebra & its Applications Type: main |
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