Eigenspaces of graphs:
Current research on the spectral theory of finite graphs may be seen as part of a wider effort to forge closer links between algebra and combinatorics (in particular between linear algebra and graph theory).This book describes how this topic can be strengthened by exploiting properties of the eigens...
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
1997
|
| Series: | Encyclopedia of mathematics and its applications
volume 66 |
| Subjects: | |
| Online Access: | BSB01 FHN01 Volltext |
| Summary: | Current research on the spectral theory of finite graphs may be seen as part of a wider effort to forge closer links between algebra and combinatorics (in particular between linear algebra and graph theory).This book describes how this topic can be strengthened by exploiting properties of the eigenspaces of adjacency matrices associated with a graph. The extension of spectral techniques proceeds at three levels: using eigenvectors associated with an arbitrary labelling of graph vertices, using geometrical invariants of eigenspaces such as graph angles and main angles, and introducing certain kinds of canonical eigenvectors by means of star partitions and star bases. One objective is to describe graphs by algebraic means as far as possible, and the book discusses the Ulam reconstruction conjecture and the graph isomorphism problem in this context. Further problems of graph reconstruction and identification are used to illustrate the importance of graph angles and star partitions in relation to graph structure. Specialists in graph theory will welcome this treatment of important new research |
| Item Description: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Physical Description: | 1 online resource (xiii, 258 pages) |
| ISBN: | 9781139086547 |
| DOI: | 10.1017/CBO9781139086547 |
Staff View
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| 505 | 8 | |a 1. A background in graph spectra -- 2. Eigenvectors of graphs -- 3. Eigenvector techniques -- 4. Graph angles -- 5. Angle techniques -- 6. Graph perturbations -- 7. Star partitions -- 8. Canonical star bases -- 9. Miscellaneous results -- App. A. Some results from matrix theory -- App. B.A table of graph angles | |
| 520 | |a Current research on the spectral theory of finite graphs may be seen as part of a wider effort to forge closer links between algebra and combinatorics (in particular between linear algebra and graph theory).This book describes how this topic can be strengthened by exploiting properties of the eigenspaces of adjacency matrices associated with a graph. The extension of spectral techniques proceeds at three levels: using eigenvectors associated with an arbitrary labelling of graph vertices, using geometrical invariants of eigenspaces such as graph angles and main angles, and introducing certain kinds of canonical eigenvectors by means of star partitions and star bases. One objective is to describe graphs by algebraic means as far as possible, and the book discusses the Ulam reconstruction conjecture and the graph isomorphism problem in this context. Further problems of graph reconstruction and identification are used to illustrate the importance of graph angles and star partitions in relation to graph structure. Specialists in graph theory will welcome this treatment of important new research | ||
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Record in the Search Index
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| any_adam_object | |
| author | Cvetković, Dragoš M. 1941- |
| author_GND | (DE-588)110230485 (DE-588)14136985X (DE-588)141369922 |
| author_facet | Cvetković, Dragoš M. 1941- |
| author_role | aut |
| author_sort | Cvetković, Dragoš M. 1941- |
| author_variant | d m c dm dmc |
| building | Verbundindex |
| bvnumber | BV043942277 |
| classification_rvk | SK 890 |
| collection | ZDB-20-CBO |
| contents | 1. A background in graph spectra -- 2. Eigenvectors of graphs -- 3. Eigenvector techniques -- 4. Graph angles -- 5. Angle techniques -- 6. Graph perturbations -- 7. Star partitions -- 8. Canonical star bases -- 9. Miscellaneous results -- App. A. Some results from matrix theory -- App. B.A table of graph angles |
| ctrlnum | (ZDB-20-CBO)CR9781139086547 (OCoLC)855562736 (DE-599)BVBBV043942277 |
| dewey-full | 511/.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511/.5 |
| dewey-search | 511/.5 |
| dewey-sort | 3511 15 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9781139086547 |
| format | Electronic eBook |
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| id | DE-604.BV043942277 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:17Z |
| institution | BVB |
| isbn | 9781139086547 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029351246 |
| oclc_num | 855562736 |
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| owner_facet | DE-12 DE-92 |
| physical | 1 online resource (xiii, 258 pages) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO |
| publishDate | 1997 |
| publishDateSearch | 1997 |
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| publisher | Cambridge University Press |
| record_format | marc |
| series2 | Encyclopedia of mathematics and its applications |
| spelling | Cvetković, Dragoš M. 1941- Verfasser (DE-588)110230485 aut Eigenspaces of graphs D. Cvetković, P. Rowlinson, S. Simić Cambridge Cambridge University Press 1997 1 online resource (xiii, 258 pages) txt rdacontent c rdamedia cr rdacarrier Encyclopedia of mathematics and its applications volume 66 Title from publisher's bibliographic system (viewed on 05 Oct 2015) 1. A background in graph spectra -- 2. Eigenvectors of graphs -- 3. Eigenvector techniques -- 4. Graph angles -- 5. Angle techniques -- 6. Graph perturbations -- 7. Star partitions -- 8. Canonical star bases -- 9. Miscellaneous results -- App. A. Some results from matrix theory -- App. B.A table of graph angles Current research on the spectral theory of finite graphs may be seen as part of a wider effort to forge closer links between algebra and combinatorics (in particular between linear algebra and graph theory).This book describes how this topic can be strengthened by exploiting properties of the eigenspaces of adjacency matrices associated with a graph. The extension of spectral techniques proceeds at three levels: using eigenvectors associated with an arbitrary labelling of graph vertices, using geometrical invariants of eigenspaces such as graph angles and main angles, and introducing certain kinds of canonical eigenvectors by means of star partitions and star bases. One objective is to describe graphs by algebraic means as far as possible, and the book discusses the Ulam reconstruction conjecture and the graph isomorphism problem in this context. Further problems of graph reconstruction and identification are used to illustrate the importance of graph angles and star partitions in relation to graph structure. Specialists in graph theory will welcome this treatment of important new research Graph theory Spectral theory (Mathematics) Spektrum Mathematik (DE-588)4182180-4 gnd rswk-swf Graphentheorie (DE-588)4113782-6 gnd rswk-swf Endlicher Graph (DE-588)4283258-5 gnd rswk-swf Spektraltheorie (DE-588)4116561-5 gnd rswk-swf Eigenvektor (DE-588)4151198-0 gnd rswk-swf Endlicher Graph (DE-588)4283258-5 s Spektraltheorie (DE-588)4116561-5 s Eigenvektor (DE-588)4151198-0 s 1\p DE-604 Graphentheorie (DE-588)4113782-6 s Spektrum Mathematik (DE-588)4182180-4 s 2\p DE-604 Rowlinson, Peter Sonstige (DE-588)14136985X oth Simić, Slobodan Sonstige (DE-588)141369922 oth Erscheint auch als Druckausgabe 978-0-521-05718-9 Erscheint auch als Druckausgabe 978-0-521-57352-8 https://doi.org/10.1017/CBO9781139086547 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Cvetković, Dragoš M. 1941- Eigenspaces of graphs 1. A background in graph spectra -- 2. Eigenvectors of graphs -- 3. Eigenvector techniques -- 4. Graph angles -- 5. Angle techniques -- 6. Graph perturbations -- 7. Star partitions -- 8. Canonical star bases -- 9. Miscellaneous results -- App. A. Some results from matrix theory -- App. B.A table of graph angles Graph theory Spectral theory (Mathematics) Spektrum Mathematik (DE-588)4182180-4 gnd Graphentheorie (DE-588)4113782-6 gnd Endlicher Graph (DE-588)4283258-5 gnd Spektraltheorie (DE-588)4116561-5 gnd Eigenvektor (DE-588)4151198-0 gnd |
| subject_GND | (DE-588)4182180-4 (DE-588)4113782-6 (DE-588)4283258-5 (DE-588)4116561-5 (DE-588)4151198-0 |
| title | Eigenspaces of graphs |
| title_auth | Eigenspaces of graphs |
| title_exact_search | Eigenspaces of graphs |
| title_full | Eigenspaces of graphs D. Cvetković, P. Rowlinson, S. Simić |
| title_fullStr | Eigenspaces of graphs D. Cvetković, P. Rowlinson, S. Simić |
| title_full_unstemmed | Eigenspaces of graphs D. Cvetković, P. Rowlinson, S. Simić |
| title_short | Eigenspaces of graphs |
| title_sort | eigenspaces of graphs |
| topic | Graph theory Spectral theory (Mathematics) Spektrum Mathematik (DE-588)4182180-4 gnd Graphentheorie (DE-588)4113782-6 gnd Endlicher Graph (DE-588)4283258-5 gnd Spektraltheorie (DE-588)4116561-5 gnd Eigenvektor (DE-588)4151198-0 gnd |
| topic_facet | Graph theory Spectral theory (Mathematics) Spektrum Mathematik Graphentheorie Endlicher Graph Spektraltheorie Eigenvektor |
| url | https://doi.org/10.1017/CBO9781139086547 |
| work_keys_str_mv | AT cvetkovicdragosm eigenspacesofgraphs AT rowlinsonpeter eigenspacesofgraphs AT simicslobodan eigenspacesofgraphs |