Topics in graph automorphisms and reconstruction:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2016
|
| Edition: | Second edition |
| Series: | London Mathematical Society lecture note series
432 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xiv,192 Seiten |
| ISBN: | 9781316610442 |
Staff View
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Record in the Search Index
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| 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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| id | DE-604.BV043587656 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:30:20Z |
| institution | BVB |
| isbn | 9781316610442 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029002159 |
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| physical | xiv,192 Seiten |
| 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- Verfasser (DE-588)173618138 aut Topics in graph automorphisms and reconstruction Josef Lauri (University of Malta), Raffaele Scapellato (Politecnico di Milano) Second edition Cambridge Cambridge University Press 2016 xiv,192 Seiten txt rdacontent n rdamedia nc rdacarrier London Mathematical Society lecture note series 432 Graph (DE-588)4021842-9 gnd rswk-swf Automorphismengruppe (DE-588)4143708-1 gnd rswk-swf Graph (DE-588)4021842-9 s Automorphismengruppe (DE-588)4143708-1 s DE-604 Scapellato, Raffaele 1955- Verfasser (DE-588)1029582386 aut London Mathematical Society lecture note series 432 (DE-604)BV000000130 432 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029002159&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lauri, Josef 1955- Scapellato, Raffaele 1955- Topics in graph automorphisms and reconstruction London Mathematical Society lecture note series Graph (DE-588)4021842-9 gnd Automorphismengruppe (DE-588)4143708-1 gnd |
| subject_GND | (DE-588)4021842-9 (DE-588)4143708-1 |
| 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 (University of Malta), Raffaele Scapellato (Politecnico di Milano) |
| title_fullStr | Topics in graph automorphisms and reconstruction Josef Lauri (University of Malta), Raffaele Scapellato (Politecnico di Milano) |
| title_full_unstemmed | Topics in graph automorphisms and reconstruction Josef Lauri (University of Malta), Raffaele Scapellato (Politecnico di Milano) |
| title_short | Topics in graph automorphisms and reconstruction |
| title_sort | topics in graph automorphisms and reconstruction |
| topic | Graph (DE-588)4021842-9 gnd Automorphismengruppe (DE-588)4143708-1 gnd |
| topic_facet | Graph Automorphismengruppe |
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