| Description |
1 online resource (378 pages) |
| Series |
London Mathematical Society Student Texts ; no. 75 |
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London Mathematical Society student texts ; no. 75.
|
| Contents |
Cover; Title; Copyright; Contents; Preface; 1 Introduction; 1.1 Graph spectra; 1.2 Some more graph-theoretic notions; 1.3 Some results from linear algebra; Exercises; Notes; 2 Graph operations and modifications; 2.1 Complement, union and join of graphs; 2.2 Coalescence and related graph compositions; 2.3 General reduction procedures; 2.4 Line graphs and related operations; 2.5 Cartesian type operations; 2.6 Spectra of graphs of particular types; Exercises; Notes; 3 Spectrum and structure; 3.1 Counting certain subgraphs; 3.2 Regularity and bipartiteness; 3.3 Connectedness and metric invariants |
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3.4 Line graphs and related graphs3.5 More on regular graphs; 3.5.1 The second largest eigenvalue; 3.5.2 The eigenvalue with second largest modulus; 3.5.3 Miscellaneous results; 3.6 Strongly regular graphs; 3.7 Distance-regular graphs; 3.8 Automorphisms and eigenspaces; 3.9 Equitable partitions, divisors and main eigenvalues; 3.10 Spectral bounds for graph invariants; 3.11 Constraints on individual eigenvalues; 3.11.1 The largest eigenvalue; 3.11.2 The second largest eigenvalue; Exercises; Notes; 4 Characterizations by spectra; 4.1 Spectral characterizations of certain classes of graphs |
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4.1.1 Elementary spectral characterizations4.1.2 Graphs with least eigenvalue -2; 4.1.3 Characterizations according to type; 4.2 Cospectral graphs and the graph isomorphism problem; 4.2.1 Examples of cospectral graphs; 4.2.2 Constructions of cospectral graphs; 4.2.3 Statistics of cospectral graphs; 4.2.4 A comparison of various graph invariants; 4.3 Characterizations by eigenvalues and angles; 4.3.1 Cospectral graphs with the same angles; 4.3.2 Constructing trees; 4.3.3 Some characterization theorems; Exercises; Notes; 5 Structure and one eigenvalue; 5.1 Star complements |
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7.5.3 Isoperimetric problems7.6 Expansion; 7.7 The normalized Laplacian matrix; 7.8 The signless Laplacian; 7.8.1 Basic properties of Q-spectra; 7.8.2 Q-eigenvalues and graph structure; 7.8.3 The largest Q-eigenvalue; Exercises; Notes; 8 Some additional results; 8.1 More on graph eigenvalues; 8.1.1 Graph perturbations; 8.1.2 Bounds on the index; 8.2 Eigenvectors and structure; 8.3 Reconstructing the characteristic polynomial; 8.4 Integral graphs; Exercises; Notes; 9 Applications; 9.1 Physics; 9.1.1 Vibration of a membrane; 9.1.2 The dimer problem; 9.2 Chemistry |
| Summary |
A self-contained introduction to the theory of graph spectra including exercises and an extensive bibliography |
| Notes |
Title from publishers bibliographic system (viewed 22 Dec 2011) |
| Bibliography |
Includes bibliographical references (pages 333-357) and indexes |
| Subject |
Graph theory.
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Matrices.
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MATHEMATICS -- Graphic Methods.
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Graph theory
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Matrices
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| Form |
Electronic book
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| Author |
Cvetković, Dragoš
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Rowlinson, Peter
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Simić, S. (Slobodan)
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| ISBN |
9780511801518 |
|
0511801513 |
|
9780521118392 |
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0521118395 |
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9781107365704 |
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1107365708 |
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9781107360792 |
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110736079X |
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