| |
|
|
|
|
|
|
|
|
1. |
Record Nr. |
UNISA996490343703316 |
|
|
Autore |
Hoppen Carlos |
|
|
Titolo |
Locating eigenvalues in graphs : algorithms and applications / / Carlos Hoppen, David P. Jacobs, and Vilmar Trevisan |
|
|
|
|
|
|
|
Pubbl/distr/stampa |
|
|
Cham, Switzerland : , : Springer, , [2022] |
|
©2022 |
|
|
|
|
|
|
|
|
|
ISBN |
|
|
|
|
|
|
Descrizione fisica |
|
1 online resource (142 pages) |
|
|
|
|
|
|
Collana |
|
SpringerBriefs in Mathematics |
|
|
|
|
|
|
Disciplina |
|
|
|
|
|
|
Soggetti |
|
Graph theory |
Teoria de grafs |
Matrius (Matemàtica) |
Llibres electrònics |
|
|
|
|
|
|
|
|
Lingua di pubblicazione |
|
|
|
|
|
|
Formato |
Materiale a stampa |
|
|
|
|
|
Livello bibliografico |
Monografia |
|
|
|
|
|
Note generali |
|
|
|
|
|
|
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. |
|
|
|
|
|
| |