02984nam 2200517 450 99649034370331620231110214215.03-031-11698-4(CKB)5850000000078525(MiAaPQ)EBC7102140(Au-PeEL)EBL7102140(PPN)264955587(EXLCZ)99585000000007852520230225d2022 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierLocating eigenvalues in graphs algorithms and applications /Carlos Hoppen, David P. Jacobs, and Vilmar TrevisanCham, Switzerland :Springer,[2022]©20221 online resource (142 pages)SpringerBriefs in Mathematics Includes index.3-031-11697-6 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.SpringerBriefs in Mathematics Graph theoryTeoria de grafsthubMatrius (Matemàtica)thubLlibres electrònicsthubGraph theory.Teoria de grafsMatrius (Matemàtica)511.5Hoppen Carlos1258097Jacobs David P.Trevisan VilmarMiAaPQMiAaPQMiAaPQBOOK996490343703316Locating eigenvalues in graphs3018505UNISA