Topics in graph automorphisms and reconstruction /:
This in-depth coverage of important areas of graph theory maintains a focus on symmetry properties of graphs. Standard topics on graph automorphisms are presented early on, while in later chapters more specialised topics are tackled, such as graphical regular representations and pseudosimilarity. Th...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge, United Kingdom :
Cambridge University Press,
2016.
|
| Ausgabe: | Second edition. |
| Schriftenreihe: | London Mathematical Society lecture note series ;
432. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | This in-depth coverage of important areas of graph theory maintains a focus on symmetry properties of graphs. Standard topics on graph automorphisms are presented early on, while in later chapters more specialised topics are tackled, such as graphical regular representations and pseudosimilarity. The final four chapters are devoted to the reconstruction problem, and here special emphasis is given to those results that involve the symmetry of graphs, many of which are not to be found in other books. This second edition expands on several of the topics found in the first edition and includes both an enriched bibliography and a wide collection of exercises. Clearer proofs are provided, as are new examples of graphs with interesting symmetry properties. Any student who masters the contents of this book will be well prepared for current research in many aspects of the theory of graph automorphisms and the reconstruction problem. |
| Beschreibung: | 1 online resource (1 volume) : illustrations |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9781316686652 1316686655 1316610446 9781316610442 |
Internformat
MARC
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| 245 | 1 | 0 | |a Topics in graph automorphisms and reconstruction / |c Josef Lauri, Raffaele Scapellato. |
| 250 | |a Second edition. | ||
| 264 | 1 | |a Cambridge, United Kingdom : |b Cambridge University Press, |c 2016. | |
| 300 | |a 1 online resource (1 volume) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
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| 490 | 1 | |a London Mathematical Society lecture note series ; |v 432 | |
| 588 | 0 | |a Print version record. | |
| 504 | |a Includes bibliographical references and index. | ||
| 520 | |a This in-depth coverage of important areas of graph theory maintains a focus on symmetry properties of graphs. Standard topics on graph automorphisms are presented early on, while in later chapters more specialised topics are tackled, such as graphical regular representations and pseudosimilarity. The final four chapters are devoted to the reconstruction problem, and here special emphasis is given to those results that involve the symmetry of graphs, many of which are not to be found in other books. This second edition expands on several of the topics found in the first edition and includes both an enriched bibliography and a wide collection of exercises. Clearer proofs are provided, as are new examples of graphs with interesting symmetry properties. Any student who masters the contents of this book will be well prepared for current research in many aspects of the theory of graph automorphisms and the reconstruction problem. | ||
| 505 | 0 | 0 | |g Machine generated contents note: |g 1. |t Graphs and Groups: Preliminaries -- |g 1.1. |t Graphs and digraphs -- |g 1.2. |t Groups -- |g 1.3. |t Graphs and groups -- |g 1.4. |t Edge-automorphisms and line-graphs -- |g 1.5. |t word on issues of computational complexity -- |g 1.6. |t Exercises -- |g 1.7. |t Notes and guide to references -- |g 2. |t Various Types of Graph Symmetry -- |g 2.1. |t Transitivity -- |g 2.2. |t Asymmetric graphs -- |g 2.3. |t Graph symmetries and the spectrum -- |g 2.4. |t Simple eigenvalues -- |g 2.5. |t Higher symmetry conditions -- |g 2.6. |t Exercises -- |g 2.7. |t Notes and guide to references -- |g 3. |t Cayley Graphs -- |g 3.1. |t Cayley colour graphs -- |g 3.2. |t Frucht's and Bouwer's Theorems -- |g 3.3. |t Cayley graphs and digraphs -- |g 3.4. |t Doyle-Holt Graph -- |g 3.5. |t Non-Cayley vertex-transitive graphs -- |g 3.6. |t Coset graphs and Sabidussi's Theorem -- |g 3.7. |t Double coset graphs and semisymmetric graphs -- |g 3.8. |t Hamiltonicity -- |g 3.9. |t Characters of abelian groups and Cayley graphs -- |g 3.10. |t Growth rates -- |g 3.11. |t Exercises -- |g 3.12. |t Notes and guide to references -- |g 4. |t Orbital Graphs and Strongly Regular Graphs -- |g 4.1. |t Definitions and basic properties -- |g 4.2. |t Rank 3 groups -- |g 4.3. |t Strongly regular graphs -- |g 4.4. |t Integrality Condition -- |g 4.5. |t Moore graphs -- |g 4.6. |t Exercises -- |g 4.7. |t Notes and guide to references -- |g 5. |t Graphical Regular Representations and Pseudosimilarity -- |g 5.1. |t Elementary results -- |g 5.2. |t Abelian groups -- |g 5.3. |t Pseudosimilarity -- |g 5.4. |t Some basic results -- |g 5.5. |t Several pairs of pseudosimilar vertices -- |g 5.6. |t Several pairs of pseudosimilar edges -- |g 5.7. |t Large sets of mutually pseudosimilar vertices -- |g 5.8. |t Exercises -- |g 5.9. |t Notes and guide to references -- |g 6. |t Products of Graphs -- |g 6.1. |t General products of graphs -- |g 6.2. |t Direct product -- |g 6.3. |t Cartesian product -- |g 6.4. |t More products -- |g 6.5. |t Stability and two-fold automorphisms -- |g 6.6. |t Additional remarks on graph products -- |g 6.7. |t Exercises -- |g 6.8. |t Notes and guide to references -- |g 7. |t Special Classes of Vertex-Transitive Graphs and Digraphs -- |g 7.1. |t Generalised Petersen graphs -- |g 7.2. |t Kneser graphs and odd graphs -- |g 7.3. |t Metacirculant graphs -- |g 7.4. |t quasi-Cayley graphs and digraphs -- |g 7.5. |t Generalised Cayley graphs -- |g 7.6. |t Exercises -- |g 7.7. |t Notes and guide to references -- |g 8. |t Reconstruction Conjectures -- |g 8.1. |t Definitions -- |g 8.2. |t Some basic results -- |g 8.3. |t Maximal planar graphs -- |g 8.4. |t Digraphs and degree-associated reconstruction -- |g 8.5. |t Exercises -- |g 8.6. |t Notes and guide to references -- |g 9. |t Reconstructing from Subdecks -- |g 9.1. |t endvertex-deck -- |g 9.2. |t Reconstruction numbers -- |g 9.3. |t characteristic polynomial deck -- |g 9.4. |t Exercises -- |g 9.5. |t Notes and guide to references -- |g 10. |t Counting Arguments in Vertex-Reconstruction -- |g 10.1. |t Kocay's Lemma -- |g 10.2. |t Counting spanning subgraphs -- |g 10.3. |t characteristic and the chromatic polynomials -- |g 10.4. |t Exercises -- |g 10.5. |t Notes and guide to references -- |g 11. |t Counting Arguments in Edge-Reconstruction -- |g 11.1. |t Definitions and notation -- |g 11.2. |t Homomorphisms of structures -- |g 11.3. |t Lovasz' and Nash-Williams' Theorems -- |g 11.4. |t Extensions -- |g 11.5. |t Exercises -- |g 11.6. |t Notes and guide to references. |
| 650 | 0 | |a Graph theory. |0 http://id.loc.gov/authorities/subjects/sh85056471 | |
| 650 | 0 | |a Automorphisms. |0 http://id.loc.gov/authorities/subjects/sh85010452 | |
| 650 | 0 | |a Reconstruction (Graph theory) |0 http://id.loc.gov/authorities/subjects/sh91002500 | |
| 650 | 6 | |a Automorphismes. | |
| 650 | 6 | |a Reconstruction (Théorie des graphes) | |
| 650 | 7 | |a MATHEMATICS |x General. |2 bisacsh | |
| 650 | 7 | |a Automorphisms |2 fast | |
| 650 | 7 | |a Graph theory |2 fast | |
| 650 | 7 | |a Reconstruction (Graph theory) |2 fast | |
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| author | Lauri, Josef, 1955- Scapellato, Raffaele, 1955- |
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| author_facet | Lauri, Josef, 1955- Scapellato, Raffaele, 1955- |
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| contents | Graphs and Groups: Preliminaries -- Graphs and digraphs -- Groups -- Graphs and groups -- Edge-automorphisms and line-graphs -- word on issues of computational complexity -- Exercises -- Notes and guide to references -- Various Types of Graph Symmetry -- Transitivity -- Asymmetric graphs -- Graph symmetries and the spectrum -- Simple eigenvalues -- Higher symmetry conditions -- Cayley Graphs -- Cayley colour graphs -- Frucht's and Bouwer's Theorems -- Cayley graphs and digraphs -- Doyle-Holt Graph -- Non-Cayley vertex-transitive graphs -- Coset graphs and Sabidussi's Theorem -- Double coset graphs and semisymmetric graphs -- Hamiltonicity -- Characters of abelian groups and Cayley graphs -- Growth rates -- Orbital Graphs and Strongly Regular Graphs -- Definitions and basic properties -- Rank 3 groups -- Strongly regular graphs -- Integrality Condition -- Moore graphs -- Graphical Regular Representations and Pseudosimilarity -- Elementary results -- Abelian groups -- Pseudosimilarity -- Some basic results -- Several pairs of pseudosimilar vertices -- Several pairs of pseudosimilar edges -- Large sets of mutually pseudosimilar vertices -- Products of Graphs -- General products of graphs -- Direct product -- Cartesian product -- More products -- Stability and two-fold automorphisms -- Additional remarks on graph products -- Special Classes of Vertex-Transitive Graphs and Digraphs -- Generalised Petersen graphs -- Kneser graphs and odd graphs -- Metacirculant graphs -- quasi-Cayley graphs and digraphs -- Generalised Cayley graphs -- Reconstruction Conjectures -- Definitions -- Maximal planar graphs -- Digraphs and degree-associated reconstruction -- Reconstructing from Subdecks -- endvertex-deck -- Reconstruction numbers -- characteristic polynomial deck -- Counting Arguments in Vertex-Reconstruction -- Kocay's Lemma -- Counting spanning subgraphs -- characteristic and the chromatic polynomials -- Counting Arguments in Edge-Reconstruction -- Definitions and notation -- Homomorphisms of structures -- Lovasz' and Nash-Williams' Theorems -- Extensions -- Notes and guide to references. |
| ctrlnum | (OCoLC)951546196 |
| 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 |
| edition | Second edition. |
| format | Electronic eBook |
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| id | ZDB-4-EBA-ocn951546196 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:27:14Z |
| institution | BVB |
| isbn | 9781316686652 1316686655 1316610446 9781316610442 |
| language | English |
| oclc_num | 951546196 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (1 volume) : illustrations |
| psigel | ZDB-4-EBA |
| publishDate | 2016 |
| publishDateSearch | 2016 |
| publishDateSort | 2016 |
| publisher | Cambridge University Press, |
| record_format | marc |
| series | London Mathematical Society lecture note series ; |
| series2 | London Mathematical Society lecture note series ; |
| spelling | Lauri, Josef, 1955- author. https://id.oclc.org/worldcat/entity/E39PCjGJ9f4txXWdvMcRXXGKBd http://id.loc.gov/authorities/names/n2002014369 Topics in graph automorphisms and reconstruction / Josef Lauri, Raffaele Scapellato. Second edition. Cambridge, United Kingdom : Cambridge University Press, 2016. 1 online resource (1 volume) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier London Mathematical Society lecture note series ; 432 Print version record. Includes bibliographical references and index. This in-depth coverage of important areas of graph theory maintains a focus on symmetry properties of graphs. Standard topics on graph automorphisms are presented early on, while in later chapters more specialised topics are tackled, such as graphical regular representations and pseudosimilarity. The final four chapters are devoted to the reconstruction problem, and here special emphasis is given to those results that involve the symmetry of graphs, many of which are not to be found in other books. This second edition expands on several of the topics found in the first edition and includes both an enriched bibliography and a wide collection of exercises. Clearer proofs are provided, as are new examples of graphs with interesting symmetry properties. Any student who masters the contents of this book will be well prepared for current research in many aspects of the theory of graph automorphisms and the reconstruction problem. Machine generated contents note: 1. Graphs and Groups: Preliminaries -- 1.1. Graphs and digraphs -- 1.2. Groups -- 1.3. Graphs and groups -- 1.4. Edge-automorphisms and line-graphs -- 1.5. word on issues of computational complexity -- 1.6. Exercises -- 1.7. Notes and guide to references -- 2. Various Types of Graph Symmetry -- 2.1. Transitivity -- 2.2. Asymmetric graphs -- 2.3. Graph symmetries and the spectrum -- 2.4. Simple eigenvalues -- 2.5. Higher symmetry conditions -- 2.6. Exercises -- 2.7. Notes and guide to references -- 3. Cayley Graphs -- 3.1. Cayley colour graphs -- 3.2. Frucht's and Bouwer's Theorems -- 3.3. Cayley graphs and digraphs -- 3.4. Doyle-Holt Graph -- 3.5. Non-Cayley vertex-transitive graphs -- 3.6. Coset graphs and Sabidussi's Theorem -- 3.7. Double coset graphs and semisymmetric graphs -- 3.8. Hamiltonicity -- 3.9. Characters of abelian groups and Cayley graphs -- 3.10. Growth rates -- 3.11. Exercises -- 3.12. Notes and guide to references -- 4. Orbital Graphs and Strongly Regular Graphs -- 4.1. Definitions and basic properties -- 4.2. Rank 3 groups -- 4.3. Strongly regular graphs -- 4.4. Integrality Condition -- 4.5. Moore graphs -- 4.6. Exercises -- 4.7. Notes and guide to references -- 5. Graphical Regular Representations and Pseudosimilarity -- 5.1. Elementary results -- 5.2. Abelian groups -- 5.3. Pseudosimilarity -- 5.4. Some basic results -- 5.5. Several pairs of pseudosimilar vertices -- 5.6. Several pairs of pseudosimilar edges -- 5.7. Large sets of mutually pseudosimilar vertices -- 5.8. Exercises -- 5.9. Notes and guide to references -- 6. Products of Graphs -- 6.1. General products of graphs -- 6.2. Direct product -- 6.3. Cartesian product -- 6.4. More products -- 6.5. Stability and two-fold automorphisms -- 6.6. Additional remarks on graph products -- 6.7. Exercises -- 6.8. Notes and guide to references -- 7. Special Classes of Vertex-Transitive Graphs and Digraphs -- 7.1. Generalised Petersen graphs -- 7.2. Kneser graphs and odd graphs -- 7.3. Metacirculant graphs -- 7.4. quasi-Cayley graphs and digraphs -- 7.5. Generalised Cayley graphs -- 7.6. Exercises -- 7.7. Notes and guide to references -- 8. Reconstruction Conjectures -- 8.1. Definitions -- 8.2. Some basic results -- 8.3. Maximal planar graphs -- 8.4. Digraphs and degree-associated reconstruction -- 8.5. Exercises -- 8.6. Notes and guide to references -- 9. Reconstructing from Subdecks -- 9.1. endvertex-deck -- 9.2. Reconstruction numbers -- 9.3. characteristic polynomial deck -- 9.4. Exercises -- 9.5. Notes and guide to references -- 10. Counting Arguments in Vertex-Reconstruction -- 10.1. Kocay's Lemma -- 10.2. Counting spanning subgraphs -- 10.3. characteristic and the chromatic polynomials -- 10.4. Exercises -- 10.5. Notes and guide to references -- 11. Counting Arguments in Edge-Reconstruction -- 11.1. Definitions and notation -- 11.2. Homomorphisms of structures -- 11.3. Lovasz' and Nash-Williams' Theorems -- 11.4. Extensions -- 11.5. Exercises -- 11.6. Notes and guide to references. Graph theory. http://id.loc.gov/authorities/subjects/sh85056471 Automorphisms. http://id.loc.gov/authorities/subjects/sh85010452 Reconstruction (Graph theory) http://id.loc.gov/authorities/subjects/sh91002500 Automorphismes. Reconstruction (Théorie des graphes) MATHEMATICS General. bisacsh Automorphisms fast Graph theory fast Reconstruction (Graph theory) fast Scapellato, Raffaele, 1955- author. https://id.oclc.org/worldcat/entity/E39PCjvDr8Dtp9tF4cdmfPvRw3 http://id.loc.gov/authorities/names/n2002014370 has work: Topics in graph automorphisms and reconstruction (Text) https://id.oclc.org/worldcat/entity/E39PCGwfpTdFWwChWbY7c6Vf4q https://id.oclc.org/worldcat/ontology/hasWork Print version: Lauri, Josef, 1955- Topics in graph automorphisms and reconstruction. 2nd edition. Cambridge : Cambridge University Press, 2016 9781316610442 (DLC) 2016014849 (OCoLC)945804259 London Mathematical Society lecture note series ; 432. http://id.loc.gov/authorities/names/n42015587 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=1230561 Volltext |
| spellingShingle | Lauri, Josef, 1955- Scapellato, Raffaele, 1955- Topics in graph automorphisms and reconstruction / London Mathematical Society lecture note series ; Graphs and Groups: Preliminaries -- Graphs and digraphs -- Groups -- Graphs and groups -- Edge-automorphisms and line-graphs -- word on issues of computational complexity -- Exercises -- Notes and guide to references -- Various Types of Graph Symmetry -- Transitivity -- Asymmetric graphs -- Graph symmetries and the spectrum -- Simple eigenvalues -- Higher symmetry conditions -- Cayley Graphs -- Cayley colour graphs -- Frucht's and Bouwer's Theorems -- Cayley graphs and digraphs -- Doyle-Holt Graph -- Non-Cayley vertex-transitive graphs -- Coset graphs and Sabidussi's Theorem -- Double coset graphs and semisymmetric graphs -- Hamiltonicity -- Characters of abelian groups and Cayley graphs -- Growth rates -- Orbital Graphs and Strongly Regular Graphs -- Definitions and basic properties -- Rank 3 groups -- Strongly regular graphs -- Integrality Condition -- Moore graphs -- Graphical Regular Representations and Pseudosimilarity -- Elementary results -- Abelian groups -- Pseudosimilarity -- Some basic results -- Several pairs of pseudosimilar vertices -- Several pairs of pseudosimilar edges -- Large sets of mutually pseudosimilar vertices -- Products of Graphs -- General products of graphs -- Direct product -- Cartesian product -- More products -- Stability and two-fold automorphisms -- Additional remarks on graph products -- Special Classes of Vertex-Transitive Graphs and Digraphs -- Generalised Petersen graphs -- Kneser graphs and odd graphs -- Metacirculant graphs -- quasi-Cayley graphs and digraphs -- Generalised Cayley graphs -- Reconstruction Conjectures -- Definitions -- Maximal planar graphs -- Digraphs and degree-associated reconstruction -- Reconstructing from Subdecks -- endvertex-deck -- Reconstruction numbers -- characteristic polynomial deck -- Counting Arguments in Vertex-Reconstruction -- Kocay's Lemma -- Counting spanning subgraphs -- characteristic and the chromatic polynomials -- Counting Arguments in Edge-Reconstruction -- Definitions and notation -- Homomorphisms of structures -- Lovasz' and Nash-Williams' Theorems -- Extensions -- Notes and guide to references. Graph theory. http://id.loc.gov/authorities/subjects/sh85056471 Automorphisms. http://id.loc.gov/authorities/subjects/sh85010452 Reconstruction (Graph theory) http://id.loc.gov/authorities/subjects/sh91002500 Automorphismes. Reconstruction (Théorie des graphes) MATHEMATICS General. bisacsh Automorphisms fast Graph theory fast Reconstruction (Graph theory) fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85056471 http://id.loc.gov/authorities/subjects/sh85010452 http://id.loc.gov/authorities/subjects/sh91002500 |
| title | Topics in graph automorphisms and reconstruction / |
| title_alt | Graphs and Groups: Preliminaries -- Graphs and digraphs -- Groups -- Graphs and groups -- Edge-automorphisms and line-graphs -- word on issues of computational complexity -- Exercises -- Notes and guide to references -- Various Types of Graph Symmetry -- Transitivity -- Asymmetric graphs -- Graph symmetries and the spectrum -- Simple eigenvalues -- Higher symmetry conditions -- Cayley Graphs -- Cayley colour graphs -- Frucht's and Bouwer's Theorems -- Cayley graphs and digraphs -- Doyle-Holt Graph -- Non-Cayley vertex-transitive graphs -- Coset graphs and Sabidussi's Theorem -- Double coset graphs and semisymmetric graphs -- Hamiltonicity -- Characters of abelian groups and Cayley graphs -- Growth rates -- Orbital Graphs and Strongly Regular Graphs -- Definitions and basic properties -- Rank 3 groups -- Strongly regular graphs -- Integrality Condition -- Moore graphs -- Graphical Regular Representations and Pseudosimilarity -- Elementary results -- Abelian groups -- Pseudosimilarity -- Some basic results -- Several pairs of pseudosimilar vertices -- Several pairs of pseudosimilar edges -- Large sets of mutually pseudosimilar vertices -- Products of Graphs -- General products of graphs -- Direct product -- Cartesian product -- More products -- Stability and two-fold automorphisms -- Additional remarks on graph products -- Special Classes of Vertex-Transitive Graphs and Digraphs -- Generalised Petersen graphs -- Kneser graphs and odd graphs -- Metacirculant graphs -- quasi-Cayley graphs and digraphs -- Generalised Cayley graphs -- Reconstruction Conjectures -- Definitions -- Maximal planar graphs -- Digraphs and degree-associated reconstruction -- Reconstructing from Subdecks -- endvertex-deck -- Reconstruction numbers -- characteristic polynomial deck -- Counting Arguments in Vertex-Reconstruction -- Kocay's Lemma -- Counting spanning subgraphs -- characteristic and the chromatic polynomials -- Counting Arguments in Edge-Reconstruction -- Definitions and notation -- Homomorphisms of structures -- Lovasz' and Nash-Williams' Theorems -- Extensions -- Notes and guide to references. |
| title_auth | Topics in graph automorphisms and reconstruction / |
| title_exact_search | Topics in graph automorphisms and reconstruction / |
| title_full | Topics in graph automorphisms and reconstruction / Josef Lauri, Raffaele Scapellato. |
| title_fullStr | Topics in graph automorphisms and reconstruction / Josef Lauri, Raffaele Scapellato. |
| title_full_unstemmed | Topics in graph automorphisms and reconstruction / Josef Lauri, Raffaele Scapellato. |
| title_short | Topics in graph automorphisms and reconstruction / |
| title_sort | topics in graph automorphisms and reconstruction |
| topic | Graph theory. http://id.loc.gov/authorities/subjects/sh85056471 Automorphisms. http://id.loc.gov/authorities/subjects/sh85010452 Reconstruction (Graph theory) http://id.loc.gov/authorities/subjects/sh91002500 Automorphismes. Reconstruction (Théorie des graphes) MATHEMATICS General. bisacsh Automorphisms fast Graph theory fast Reconstruction (Graph theory) fast |
| topic_facet | Graph theory. Automorphisms. Reconstruction (Graph theory) Automorphismes. Reconstruction (Théorie des graphes) MATHEMATICS General. Automorphisms Graph theory |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=1230561 |
| work_keys_str_mv | AT laurijosef topicsingraphautomorphismsandreconstruction AT scapellatoraffaele topicsingraphautomorphismsandreconstruction |