Academic Journal
The Multiplicity of Eigenvalues of Aα of Trees.
| Τίτλος: | The Multiplicity of Eigenvalues of Aα of Trees. |
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| Συγγραφείς: | Du, Zhibin1,2 (AUTHOR) zhibindu@m.scnu.edu.cn |
| Πηγή: | Annals of Combinatorics. Sep2026, Vol. 30 Issue 3, p945-964. 20p. |
| Θεματικοί όροι: | *Eigenvalues, *Multiplicity (Mathematics), *Tree graphs, *Linear algebra, *Matrices (Mathematics), *Laplacian matrices |
| Περίληψη: | Let T be a tree on n vertices. For α ∈ [ 0 , 1) , let A α (T) = α D (T) + (1 - α) A (T) , where D(T) is the degree diagonal matrix of T and A(T) is the adjacency matrix of T. Denote by m A α (T) , θ the multiplicity of θ as an eigenvalue of A α (T). When α = 1 2 (aiming to the Laplacian matrix of T), it is known in Akbari et al. (Linear Algebra Appl 586:262–273, 2020) that m A α (T) , θ ≤ n - 3 2 , and when α = 0 (aiming to the adjacency matrix of T), the upper bound of m A α (T) , θ for any fixed real number θ was recently obtained in Du and Huang (Linear Algebra Appl 654:56–68, 2022). In this paper, we establish an upper bound of m A α (T) , θ for any α ∈ [ 0 , 1) and any fixed real number θ , unifying and generalizing the above-mentioned results about the multiplicities of eigenvalues of the adjacency matrix and Laplacian matrix of trees. [ABSTRACT FROM AUTHOR] |
| Βάση Δεδομένων: | Academic Search Index |
| FullText | Text: Availability: 0 |
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| Header | DbId: asx DbLabel: Academic Search Index An: 197188964 RelevancyScore: 1452 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 1452.42749023438 |
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| Items | – Name: Title Label: Title Group: Ti Data: The Multiplicity of Eigenvalues of Aα of Trees. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Du%2C+Zhibin%22">Du, Zhibin</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> zhibindu@m.scnu.edu.cn</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Annals+of+Combinatorics%22">Annals of Combinatorics</searchLink>. Sep2026, Vol. 30 Issue 3, p945-964. 20p. – Name: Subject Label: Subject Terms Group: Su Data: *<searchLink fieldCode="DE" term="%22Eigenvalues%22">Eigenvalues</searchLink><br />*<searchLink fieldCode="DE" term="%22Multiplicity+%28Mathematics%29%22">Multiplicity (Mathematics)</searchLink><br />*<searchLink fieldCode="DE" term="%22Tree+graphs%22">Tree graphs</searchLink><br />*<searchLink fieldCode="DE" term="%22Linear+algebra%22">Linear algebra</searchLink><br />*<searchLink fieldCode="DE" term="%22Matrices+%28Mathematics%29%22">Matrices (Mathematics)</searchLink><br />*<searchLink fieldCode="DE" term="%22Laplacian+matrices%22">Laplacian matrices</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Let T be a tree on n vertices. For α ∈ [ 0 , 1) , let A α (T) = α D (T) + (1 - α) A (T) , where D(T) is the degree diagonal matrix of T and A(T) is the adjacency matrix of T. Denote by m A α (T) , θ the multiplicity of θ as an eigenvalue of A α (T). When α = 1 2 (aiming to the Laplacian matrix of T), it is known in Akbari et al. (Linear Algebra Appl 586:262–273, 2020) that m A α (T) , θ ≤ n - 3 2 , and when α = 0 (aiming to the adjacency matrix of T), the upper bound of m A α (T) , θ for any fixed real number θ was recently obtained in Du and Huang (Linear Algebra Appl 654:56–68, 2022). In this paper, we establish an upper bound of m A α (T) , θ for any α ∈ [ 0 , 1) and any fixed real number θ , unifying and generalizing the above-mentioned results about the multiplicities of eigenvalues of the adjacency matrix and Laplacian matrix of trees. [ABSTRACT FROM AUTHOR] |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s00026-025-00796-5 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 20 StartPage: 945 Subjects: – SubjectFull: Eigenvalues Type: general – SubjectFull: Multiplicity (Mathematics) Type: general – SubjectFull: Tree graphs Type: general – SubjectFull: Linear algebra Type: general – SubjectFull: Matrices (Mathematics) Type: general – SubjectFull: Laplacian matrices Type: general Titles: – TitleFull: The Multiplicity of Eigenvalues of Aα of Trees. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Du, Zhibin IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 09 Text: Sep2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 02180006 Numbering: – Type: volume Value: 30 – Type: issue Value: 3 Titles: – TitleFull: Annals of Combinatorics Type: main |
| ResultId | 1 |