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Record Nr. |
UNINA9910595054103321 |
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Autore |
Hoppen Carlos |
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Titolo |
Locating eigenvalues in graphs : algorithms and applications / / Carlos Hoppen, David P. Jacobs, and Vilmar Trevisan |
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Pubbl/distr/stampa |
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Cham, Switzerland : , : Springer, , [2022] |
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©2022 |
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ISBN |
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Descrizione fisica |
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1 online resource (142 pages) |
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Collana |
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SpringerBriefs in Mathematics |
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Disciplina |
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Soggetti |
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Graph theory |
Teoria de grafs |
Matrius (Matemàtica) |
Llibres electrònics |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Nota di contenuto |
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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 |
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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. |
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