LEADER 02984nam 2200517 450 001 996490343703316 005 20231110214215.0 010 $a3-031-11698-4 035 $a(CKB)5850000000078525 035 $a(MiAaPQ)EBC7102140 035 $a(Au-PeEL)EBL7102140 035 $a(PPN)264955587 035 $a(EXLCZ)995850000000078525 100 $a20230225d2022 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aLocating eigenvalues in graphs $ealgorithms and applications /$fCarlos Hoppen, David P. Jacobs, and Vilmar Trevisan 210 1$aCham, Switzerland :$cSpringer,$d[2022] 210 4$dŠ2022 215 $a1 online resource (142 pages) 225 1 $aSpringerBriefs in Mathematics 300 $aIncludes index. 311 $a3-031-11697-6 327 $aIntro -- Preface -- Acknowledgments -- Contents -- 1 Introduction -- References -- 2 Preliminaries -- 2.1 Graph Theory Review -- 2.2 Linear Algebra Review -- 2.3 Eigenvalues and Eigenvectors -- 2.4 Elementary Matrices and Operations -- 2.5 Spectral Graph Theory -- 2.6 Sylvester's Law of Inertia -- 2.7 Analysis of Algorithms -- 2.8 Rooted Trees -- References -- 3 Locating Eigenvalues in Trees -- 3.1 Adjacency Matrix -- 3.2 Symmetric Matrices with Underlying Tree -- 3.3 Laplacian Matrix and Applications -- References -- 4 Graph Classes and Graph Decompositions -- 4.1 Hereditary Graph Classes -- 4.2 Cographs -- 4.3 Tree Decomposition -- 4.4 Nice Tree Decomposition -- 4.5 Clique Decomposition -- 4.6 Slick Clique Decomposition -- References -- 5 Locating Eigenvalues in Cographs -- 5.1 Diagonalizing a Row and Column -- 5.2 Diagonalizing A + xI -- 5.3 Applications: Inertia and Spectral Characterization of Cographs -- References -- 6 Locating Eigenvalues Using Tree Decomposition -- 6.1 Gaussian Elimination and Tree Decompositions -- 6.2 Diagonalization Algorithm -- 6.3 Example -- References -- 7 Locating Eigenvalues Using Slick Clique Decomposition -- 7.1 Clique-Width and Diagonalization -- 7.2 The Algorithm -- 7.3 Example -- 7.4 Correctness, Complexity, and Implementation -- References -- 8 Distance-Hereditary Graphs -- 8.1 Distance-Hereditary Graphs -- 8.2 Locating Eigenvalues in Distance-Hereditary Graphs -- 8.3 The Graphs Having scw ?2 -- References -- Index. 410 0$aSpringerBriefs in Mathematics 606 $aGraph theory 606 $aTeoria de grafs$2thub 606 $aMatrius (Matemātica)$2thub 608 $aLlibres electrōnics$2thub 615 0$aGraph theory. 615 7$aTeoria de grafs 615 7$aMatrius (Matemātica) 676 $a511.5 700 $aHoppen$b Carlos$01258097 702 $aJacobs$b David P. 702 $aTrevisan$b Vilmar 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996490343703316 996 $aLocating eigenvalues in graphs$93018505 997 $aUNISA