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...
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2016
|
| Edition: | Second edition |
| Series: | London Mathematical Society lecture note series
432 |
| Subjects: | |
| Online Access: | BSB01 FHN01 Volltext Inhaltsverzeichnis |
| Summary: | 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 |
| Item Description: | Title from publisher's bibliographic system (viewed on 06 Jun 2016) |
| Physical Description: | 1 online resource (xiv, 192 pages) |
| ISBN: | 9781316669846 |
| DOI: | 10.1017/CBO9781316669846 |
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Record in the Search Index
| _version_ | 1804176880638623744 |
|---|---|
| adam_text | Titel: Topics in graph automorphisms and reconstruction
Autor: Lauri, Josef
Jahr: 2016
Contents
Preface to the Second Edition page xi
Preface to the First Edition xiii
1 Graphs and Groups: Preliminaries 1
1.1 Graphs and digraphs 1
1.2 Groups 3
1.3 Graphs and groups 7
1.4 Edge-automorphisms and line-graphs 10
1.5 A word on issues of computational complexity 13
1.6 Exercises 15
1.7 Notes and guide to references 17
2 Various T^pes of Graph Symmetry 18
2.1 Transitivity 18
2.2 Asymmetric graphs 25
2.3 Graph symmetries and the spectrum 29
2.4 Simple eigenvalues 31
2.5 Higher symmetry conditions 32
2.6 Exercises 35
2.7 Notes and guide to references 38
3 Cayley Graphs 39
3.1 Cayley colour graphs 39
3.2 Frucht s and Bouwer s Theorems 42
3.3 Cayley graphs and digraphs 44
3.4 The Doyle-Holt Graph 47
3.5 Non-Cayley vertex-transitive graphs 48
3.6 Coset graphs and Sabidussi s Theorem 49
3.7 Double coset graphs and semisymmetric graphs 51
vii
viii
Contents
3.8 Hamiltonicity 53
3.9 Characters of abelian groups and Cayley graphs 55
3.10 Growth rates 56
3.11 Exercises 58
3.12 Notes and guide to references 62
4 Orbital Graphs and Strongly Regular Graphs 64
4.1 Definitions and basic properties 64
4.2 Rank 3 groups 68
4.3 Strongly regular graphs 69
4.4 The Integrality Condition 70
4.5 Moore graphs 73
4.6 Exercises 75
4.7 Notes and guide to references 77
5 Graphical Regular Representations and Pseudosimilarity 79
5.1 Elementary results 79
5.2 Abelian groups 80
5.3 Pseudosimilarity 81
5.4 Some basic results 82
5.5 Several pairs of pseudosimilar vertices 84
5.6 Several pairs of pseudosimilar edges 85
5.7 Large sets of mutually pseudosimilar vertices 86
5.8 Exercises 88
5.9 Notes and guide to references 91
6 Products of Graphs 92
6.1 General products of graphs 93
6.2 Direct product 95
6.3 Cartesian product 97
6.4 More products 99
6.5 Stability and two-fold automorphisms 102
6.6 Additional remarks on graph products 105
6.7 Exercises 105
6.8 Notes and guide to references 108
7 Special Classes of Vertex-Transitive Graphs and Digraphs 109
7.1 Generalised Petersen graphs 110
7.2 Kneser graphs and odd graphs 114
7.3 Metacirculant graphs 115
7.4 The quasi-Cayley graphs and digraphs 117
7.5 Generalised Cayley graphs 119
Contents ix
7.6 Exercises 120
7.7 Notes and guide to references 122
8 The Reconstruction Conjectures 123
8.1 Definitions 124
8.2 Some basic results 126
8.3 Maximal planar graphs 132
8.4 Digraphs and degree-associated reconstruction 136
8.5 Exercises 138
8.6 Notes and guide to references 139
9 Reconstructing from Subdecks 140
9.1 The endvertex-deck 140
9.2 Reconstruction numbers 141
9.3 The characteristic polynomial deck 144
9.4 Exercises 147
9.5 Notes and guide to references 147
10 Counting Arguments in Vertex-Reconstruction 149
10.1 Kocay s Lemma 149
10.2 Counting spanning subgraphs 151
10.3 The characteristic and the chromatic polynomials 154
10.4 Exercises 155
10.5 Notes and guide to references 156
11 Counting Arguments in Edge-Reconstruction 157
11.1 Definitions and notation 157
11.2 Homomorphisms of structures 159
11.3 Lovász and Nash-Williams Theorems 163
11.4 Extensions 166
11.5 Exercises 168
11.6 Notes and guide to references 169
References 171
List of Notations 185
Index of Terms and Definitions 187
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| isbn | 9781316669846 |
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| spelling | Lauri, Josef 1955- Verfasser aut Topics in graph automorphisms and reconstruction Josef Lauri, Raffaele Scapellato Second edition Cambridge Cambridge University Press 2016 1 online resource (xiv, 192 pages) txt rdacontent c rdamedia cr rdacarrier London Mathematical Society lecture note series 432 Title from publisher's bibliographic system (viewed on 06 Jun 2016) 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 Graph theory Automorphisms Reconstruction (Graph theory) Automorphismengruppe (DE-588)4143708-1 gnd rswk-swf Graph (DE-588)4021842-9 gnd rswk-swf Graph (DE-588)4021842-9 s Automorphismengruppe (DE-588)4143708-1 s 1\p DE-604 Scapellato, Raffaele 1955- Sonstige oth Erscheint auch als Druckausgabe 978-1-316-61044-2 https://doi.org/10.1017/CBO9781316669846 Verlag URL des Erstveröffentlichers Volltext HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029349257&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Lauri, Josef 1955- Topics in graph automorphisms and reconstruction Graph theory Automorphisms Reconstruction (Graph theory) Automorphismengruppe (DE-588)4143708-1 gnd Graph (DE-588)4021842-9 gnd |
| subject_GND | (DE-588)4143708-1 (DE-588)4021842-9 |
| title | Topics in graph automorphisms and reconstruction |
| 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 Automorphisms Reconstruction (Graph theory) Automorphismengruppe (DE-588)4143708-1 gnd Graph (DE-588)4021842-9 gnd |
| topic_facet | Graph theory Automorphisms Reconstruction (Graph theory) Automorphismengruppe Graph |
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