Recent results in the theory of graph spectra: Includes indexes
Gespeichert in:
| Format: | Elektronisch E-Book |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Amsterdam
North-Holland
1988
|
| Schriftenreihe: | Annals of discrete mathematics
36 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 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 combinatorial objects (including distance regular and distance transitive graphs, association schemes, and block designs) have made use of eigenvalue techniques, usually as a method to show the nonexistence of objects with certain parameters. The basic method is to construct a graph which contains the structure of the combinatorial object and then to use the properties of the eigenvalues of the graph. Methods of this type are given in Chapter 2. Several topics have been included in Chapter 3, including the relationships between the spectrum and automorphism group of a graph, the graph isomorphism and the graph reconstruction problem, spectra of random graphs, and the Shannon capacity problem. Some graph polynomials related to the characteristic polynomial are described in Chapter 4. These include the matching, distance, and permanental polynomials. Applications of the theory of graph spectra to Chemistry and other branches of science are described from a mathematical viewpoint in Chapter 5. The last chapter is devoted to the extension of the theory of graph spectra to infinite graphs Includes bibliographical references (p. 233-290) |
| Beschreibung: | 1 Online-Ressource (1 online resource (xi, 306 p.)) |
| ISBN: | 9780444703613 0444703616 |
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| 245 | 1 | 0 | |a Recent results in the theory of graph spectra |b Includes indexes |c Dragos M. Cvetkovic ... [et al.] |
| 246 | 1 | 3 | |a Graph spectra |
| 264 | 1 | |a Amsterdam |b North-Holland |c 1988 | |
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| 490 | 0 | |a Annals of discrete mathematics |v 36 | |
| 500 | |a 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 combinatorial objects (including distance regular and distance transitive graphs, association schemes, and block designs) have made use of eigenvalue techniques, usually as a method to show the nonexistence of objects with certain parameters. The basic method is to construct a graph which contains the structure of the combinatorial object and then to use the properties of the eigenvalues of the graph. Methods of this type are given in Chapter 2. Several topics have been included in Chapter 3, including the relationships between the spectrum and automorphism group of a graph, the graph isomorphism and the graph reconstruction problem, spectra of random graphs, and the Shannon capacity problem. Some graph polynomials related to the characteristic polynomial are described in Chapter 4. These include the matching, distance, and permanental polynomials. Applications of the theory of graph spectra to Chemistry and other branches of science are described from a mathematical viewpoint in Chapter 5. The last chapter is devoted to the extension of the theory of graph spectra to infinite graphs | ||
| 500 | |a Includes bibliographical references (p. 233-290) | ||
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| isbn | 9780444703613 0444703616 |
| language | English |
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| spelling | Recent results in the theory of graph spectra Includes indexes Dragos M. Cvetkovic ... [et al.] Graph spectra Amsterdam North-Holland 1988 1 Online-Ressource (1 online resource (xi, 306 p.)) txt rdacontent c rdamedia cr rdacarrier Annals of discrete mathematics 36 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 combinatorial objects (including distance regular and distance transitive graphs, association schemes, and block designs) have made use of eigenvalue techniques, usually as a method to show the nonexistence of objects with certain parameters. The basic method is to construct a graph which contains the structure of the combinatorial object and then to use the properties of the eigenvalues of the graph. Methods of this type are given in Chapter 2. Several topics have been included in Chapter 3, including the relationships between the spectrum and automorphism group of a graph, the graph isomorphism and the graph reconstruction problem, spectra of random graphs, and the Shannon capacity problem. Some graph polynomials related to the characteristic polynomial are described in Chapter 4. These include the matching, distance, and permanental polynomials. Applications of the theory of graph spectra to Chemistry and other branches of science are described from a mathematical viewpoint in Chapter 5. The last chapter is devoted to the extension of the theory of graph spectra to infinite graphs Includes bibliographical references (p. 233-290) Graphes, Theorie des ram Matrices ram Graph theory Matrices Graphes, Theorie des Graphes, Theorie des / ram Matrices / ram Spektrum (DE-588)4056139-2 gnd rswk-swf Graph (DE-588)4021842-9 gnd rswk-swf Spektrale Graphentheorie (DE-588)1201434653 gnd rswk-swf Spektrale Graphentheorie (DE-588)1201434653 s Graph (DE-588)4021842-9 s Spektrum (DE-588)4056139-2 s 1\p DE-604 Cvetkovic, Dragos M. Sonstige oth http://www.sciencedirect.com/science/book/9780444703613 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Recent results in the theory of graph spectra Includes indexes Graphes, Theorie des ram Matrices ram Graph theory Matrices Graphes, Theorie des Graphes, Theorie des / ram Matrices / ram Spektrum (DE-588)4056139-2 gnd Graph (DE-588)4021842-9 gnd Spektrale Graphentheorie (DE-588)1201434653 gnd |
| subject_GND | (DE-588)4056139-2 (DE-588)4021842-9 (DE-588)1201434653 |
| title | Recent results in the theory of graph spectra Includes indexes |
| title_alt | Graph spectra |
| title_auth | Recent results in the theory of graph spectra Includes indexes |
| title_exact_search | Recent results in the theory of graph spectra Includes indexes |
| title_full | Recent results in the theory of graph spectra Includes indexes Dragos M. Cvetkovic ... [et al.] |
| title_fullStr | Recent results in the theory of graph spectra Includes indexes Dragos M. Cvetkovic ... [et al.] |
| title_full_unstemmed | Recent results in the theory of graph spectra Includes indexes Dragos M. Cvetkovic ... [et al.] |
| title_short | Recent results in the theory of graph spectra |
| title_sort | recent results in the theory of graph spectra includes indexes |
| title_sub | Includes indexes |
| topic | Graphes, Theorie des ram Matrices ram Graph theory Matrices Graphes, Theorie des Graphes, Theorie des / ram Matrices / ram Spektrum (DE-588)4056139-2 gnd Graph (DE-588)4021842-9 gnd Spektrale Graphentheorie (DE-588)1201434653 gnd |
| topic_facet | Graphes, Theorie des Matrices Graph theory Graphes, Theorie des / ram Matrices / ram Spektrum Graph Spektrale Graphentheorie |
| url | http://www.sciencedirect.com/science/book/9780444703613 |
| work_keys_str_mv | AT cvetkovicdragosm recentresultsinthetheoryofgraphspectraincludesindexes AT cvetkovicdragosm graphspectra |