Topics in graph automorphisms and reconstruction:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge University Press
2003
|
| Ausgabe: | 1. publication |
| Schriftenreihe: | London Mathematical Society Student Texts
54 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | XII, 159 Seiten graph. Darst. |
| ISBN: | 0521529034 0521821517 |
Internformat
MARC
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| 245 | 1 | 0 | |a Topics in graph automorphisms and reconstruction |c Josef Lauri, University of Malta, Raffaele Scapellato, Politecnico di Milano |
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Datensatz im Suchindex
| _version_ | 1804144926438457344 |
|---|---|
| adam_text | Contents
Preface
page
xi
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
14
1.6
Exercises
16
1.7
Notes and guide to references
17
2
Various Types of Graph Symmetry
19
2.1
Transitivity
19
2.2
Asymmetric graphs
24
2.3
Graph symmetries and the spectrum
27
2.4
Simple eigenvalues
29
2.5
Higher symmetry conditions
30
2.6
Exercises
33
2.7
Notes and guide to references
35
3
Cayley Graphs
36
3.1
Cayley colour graphs
36
3.2 Frucht
s and
Bouwers
Theorems
39
3.3
Cayley graphs and digraphs
42
3.4
Non-Cayley vertex-transitive graphs
44
3.5
Coset graphs and Sabidussi s Theorem
45
3.6
Hamiltonicity
47
3.7
Growth rates
48
3.8
Exercises
50
3.9
Notes and guide to references
52
viii Contents
4
Orbital
Graphs and Strongly Regular Graphs
55
4.1
Definitions and basic properties
55
4.2
Rank
3
groups
59
4.3
Strongly regular graphs
60
4.4
The Integrality Condition
61
4.5
Moore Graphs
63
4.6
Exercises
64
4.7
Notes and guide to references
65
5
Graphical Regular Representations and Pseudosimi-
larity
66
5.1
Elementary results
66
5.2
Abelian groups
67
5.3
Pseudosimilarity
68
5.4
Some basic results
69
5.5
Several pairs pseudosimilar
71
5.6
Mutually pseudosimilar vertices
72
5.7
Exercises
73
5.8
Notes and guide to references
76
6
Products of Graphs
77
6.1
General products of graphs
78
6.2
Categorical product
79
6.3
Cartesian product
80
6.4
More products
83
6.5
Additional remarks
86
6.6
Exercises
86
6.7
Notes and guide to references
87
7
Special Classes of Vertex-Transitive Graphs and Di¬
graphs
88
7.1
Generalised Petersen graphs
89
7.2
K neser
graphs and odd graphs
93
7.3
Metacirculant graphs
94
7.4
The quasi-Caylev graphs and digraphs
96
7.5
Exercises
99
7.6
Notes and guide to references
100
8
The Reconstruction Conjectures
102
8.1
Definitions
103
S.
2
Some basic results
105
».3
Maximal planar graphs
110
ьЛ
Exercises
111
Contents ix
8.5 Notes
and guide to references
112
9
Reconstructing from Subdecks
114
9.1
The endvertex-deck
114
9.2
Reconstruction numbers
116
9.3
The characteristic polynomial deck
117
9.4
Exercises
119
9.5
Notes and guide to references
120
10
Counting Arguments in Vertex-Reconstruction
121
10.1
Kocay s Lemma
121
10.2
Counting spanning subgraphs
123
10.3
The characteristic and the chromatic polynomials
126
10.4
Exercises
127
10.5
Notes and guide to references
128
11
Counting Arguments in Edge-Reconstruction
129
11.1
Definitions and notation
129
11.2
Homomorphisms of structures
132
11.3
Lovász
and Nash-Williams Theorems
135
11.4
Extensions
138
11.5
Exercises
140
11.6
Notes and guide to references
141
Bibliography
143
List of Notation
153
Index of Terms and Definitions
155
The aim of this book is to provide in-depth coverage of selected areas of
graph theory, and throughout the focus is mainly 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 four final chapters are
devoted to the reconstruction problem, and here greater emphasis is given
to those results that involve the symmetry of graphs.
As much as possible, the authors have tried to present results and proofs
that are not often to be found in other textbooks. Any student who has mas¬
tered 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.
Josef
Lauri
is Professor of Mathematics at the University of Malta.
Raffaele
Scapellato is Professor of Geometry at
Politecnico di Milano.
London Mathematical Society
Student Texts
Edited by PROFESSOR
C. M.
SERIES, Mathematics Institute, University of
Warwick, Coventry CV4 7AL, United Kingdom
with assistance from
E. Rees
(Edinburghi
P. Olver (Minnesota)
M. Liebeck (Imperial) J. D. Gibbon (Imperial)
This series consists of textbooks aimed at advanced undergrade
ning
graduate students. It covers the whole range of pure mathematics, as
well as topics in applied mathematics and mathematical physics that involve a
substantial use of modern mathematical methods.
Topics not of a standard nature though of current interest are also covered by
volumes in this series.
Cambridge
UNIVERSITY PRESS
www.cambridge.org
ISBN
0-521-52903-4
780521
|
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| isbn | 0521529034 0521821517 |
| language | English |
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| 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 1. publication Cambridge [u.a.] Cambridge University Press 2003 XII, 159 Seiten graph. Darst. txt rdacontent n rdamedia nc rdacarrier London Mathematical Society Student Texts 54 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 1\p DE-604 Scapellato, Raffaele 1955- Verfasser (DE-588)1029582386 aut London Mathematical Society Student Texts 54 (DE-604)BV000841726 54 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021980875&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021980875&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Lauri, Josef 1955- Scapellato, Raffaele 1955- Topics in graph automorphisms and reconstruction London Mathematical Society Student Texts 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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| volume_link | (DE-604)BV000841726 |
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