Locating eigenvalues in graphs : algorithms and applications / / Carlos Hoppen, David P. Jacobs, and Vilmar Trevisan
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| Autore: |
Hoppen Carlos
|
| Titolo: |
Locating eigenvalues in graphs : algorithms and applications / / Carlos Hoppen, David P. Jacobs, and Vilmar Trevisan
|
| Pubblicazione: | Cham, Switzerland : , : Springer, , [2022] |
| ©2022 | |
| Descrizione fisica: | 1 online resource (142 pages) |
| Disciplina: | 511.5 |
| Soggetto topico: | Graph theory |
| Teoria de grafs | |
| Matrius (Matemàtica) | |
| Soggetto genere / forma: | Llibres electrònics |
| Persona (resp. second.): | JacobsDavid P. |
| TrevisanVilmar | |
| Note generali: | Includes index. |
| Nota di contenuto: | Intro -- Preface -- Acknowledgments -- Contents -- 1 Introduction -- References -- 2 Preliminaries -- 2.1 Graph Theory Review -- 2.2 Linear Algebra Review -- 2.3 Eigenvalues and Eigenvectors -- 2.4 Elementary Matrices and Operations -- 2.5 Spectral Graph Theory -- 2.6 Sylvester's Law of Inertia -- 2.7 Analysis of Algorithms -- 2.8 Rooted Trees -- References -- 3 Locating Eigenvalues in Trees -- 3.1 Adjacency Matrix -- 3.2 Symmetric Matrices with Underlying Tree -- 3.3 Laplacian Matrix and Applications -- References -- 4 Graph Classes and Graph Decompositions -- 4.1 Hereditary Graph Classes -- 4.2 Cographs -- 4.3 Tree Decomposition -- 4.4 Nice Tree Decomposition -- 4.5 Clique Decomposition -- 4.6 Slick Clique Decomposition -- References -- 5 Locating Eigenvalues in Cographs -- 5.1 Diagonalizing a Row and Column -- 5.2 Diagonalizing A + xI -- 5.3 Applications: Inertia and Spectral Characterization of Cographs -- References -- 6 Locating Eigenvalues Using Tree Decomposition -- 6.1 Gaussian Elimination and Tree Decompositions -- 6.2 Diagonalization Algorithm -- 6.3 Example -- References -- 7 Locating Eigenvalues Using Slick Clique Decomposition -- 7.1 Clique-Width and Diagonalization -- 7.2 The Algorithm -- 7.3 Example -- 7.4 Correctness, Complexity, and Implementation -- References -- 8 Distance-Hereditary Graphs -- 8.1 Distance-Hereditary Graphs -- 8.2 Locating Eigenvalues in Distance-Hereditary Graphs -- 8.3 The Graphs Having scw ≤2 -- References -- Index. |
| Titolo autorizzato: | Locating eigenvalues in graphs |
| ISBN: | 3-031-11698-4 |
| Formato: | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione: | Inglese |
| Record Nr.: | 9910595054103321 |
| Lo trovi qui: | Univ. Federico II |
| Opac: | Controlla la disponibilità qui |
Serie:
SpringerBriefs in Mathematics