UID:
almahu_9947367768502882
Umfang:
1 online resource (319 p.)
ISBN:
1-281-79315-9
,
9786611793159
,
0-08-086776-6
Serie:
Annals of discrete mathematics ; 36
Inhalt:
The purpose of this volume is to review the results in spectral graph theory which have appeared since 1978.The problem of characterizing graphs with least eigenvalue -2 was one of the original problems of spectral graph theory. The techniques used in the investigation of this problem have continued to be useful in other contexts including forbidden subgraph techniques as well as geometric methods involving root systems. In the meantime, the particular problem giving rise to these methods has been solved almost completely. This is indicated in Chapter 1.The study of various com
Anmerkung:
Description based upon print version of record.
,
Front Cover; Recent Results in the Theory of Graph Spectra; Copyright Page; Contents; Introduction; Chapter 1. Characterizations of Graphs by their Spectra; 1.1. Generalized Line Graphs and Graphs with Least Eigenvalue -2; 1.2. Other Graph Characterizations; 1.3. Cospectral Constructions; 1.4. Hereditary Characterizations; Chapter 2. Distance-Regular and Similar Graphs; 2.1. The Bose-Mesner Algebra; 2.2. Moore Graphs and their Generalizations; 2.3. Distance-Transitive Graphs; 2.4. Distance-Regular Graphs and other Combinatorial Objects; 2.5. Root Systems and Distance-Regular Graphs
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Chapter 3. Miscellaneous Results from the Theory of Graph Spectra3.1. The Sachs Theorem; 3.2. Spectra of Graphs Derived by Operations and Transformations; 3.3. Constructions of Graphs Using Spectra; 3.4. The Automorphism Group and the Spectrum of a Graph; 3.5. Identification and Reconstruction of Graphs; 3.6. The Shannon Capacity and Spectral Bounds for Graph Invariants; 3.7. Spectra of Random Graphs; 3.8. The Number of Walks in a Graph; 3.9. The Number of Spanning Trees in a Graph; 3.10. The Use of Spectra to Solve Graph Equations; 3.11. Spectra of Tournaments; 3.12. Other Results
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Chapter 4. The Matching Polynomial and Other Graph Polynomials4.1. The Matching Polynomial; 4.2. The Matching Polynomial of Weighted Graphs; 4.3. The Rook Polynomial; 4.4. The Independence Polynomial; 4.5. The F-Polynomial; 4.6. The Permanental Polynomial; 4.7. Polynomials and the Admittance Matrix; 4.8. The Distance Polynomial; 4.9. Miscellaneous Results; Chapter 5. Applications to Chemistry and Other Branches of Science; 5.1. On Hückel Molecular Orbital Theory; 5.2. The Characteristic Polynomial; 5.3. Cospectral Molecular Graphs
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5.4. The Spectrum and the Automorphism Group of Molecular Graphs5.5. The Energy of a Graph; 5.6. S- and T- Isomers; 5.7. Circuits and the Energy of a Graph; 5.8. Charge and Bond Order; 5.9. HOMO-LUMO Separation; 5.10. The Determinant of the Adjacency Matrix; 5.11. The Magnetic Properties of Conjugated Hydrocarbons; 5.12. The Topological Resonance Energy; 5.13. Some Spectral Properties of Hexagonal Systems; 5.14. Miscellaneous HMO Results; 5.15. Molecular Orbital Approaches Other than the HMO Model
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5.16. Applications of Graph Eigenvalues in Physics and Chemistry Other than Molecular Orbital Models5.17. Graph Eigenvalues in Geography and the Social Sciences; Chapter 6. Spectra of Infinite Graphs; 6.1. General Properties; 6.2. Spectral Properties of some Classes of Infinite Graphs; 6.3. The Characteristic Function of an Infinite Graph; 6.4. Graphs with a Finite Spectrum; 6.5. Operations on Infinite Graphs; 6.6. The Automorphism Group of an Infinite Graph; 6.7. Infinite Generalized Line Graphs; 6.8. The D-spectrum of Infinite Graphs; 6.9. Graphs with Uniformly Bounded Spectra
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6.10. Another Approach to the Spectrum of an Infinite Graph
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English
Weitere Ausg.:
ISBN 0-444-70361-6
Sprache:
Englisch
