Topics in algebraic graph theory:
"This book contains ten expository chapters written by acknowledged international experts in the field. Their well-written contributions have been carefully edited to enhance readability and to standardize the chapter structure, terminology and notation throughout the book. To help the reader,...
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge University Press
2004
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Encyclopedia of mathematics and its applications
102 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | "This book contains ten expository chapters written by acknowledged international experts in the field. Their well-written contributions have been carefully edited to enhance readability and to standardize the chapter structure, terminology and notation throughout the book. To help the reader, there is an extensive introductory chapter that covers the basic background material in graph theory, linear algebra and group theory. Each chapter concludes with an extensive list of references."--BOOK JACKET. |
| Beschreibung: | XV, 276 S. graph. Darst. |
| ISBN: | 0521801974 |
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Datensatz im Suchindex
| _version_ | 1804133238122217472 |
|---|---|
| adam_text | Titel: Topics in algebraic graph theory
Autor: Beineke, Lowell W
Jahr: 2004
Contents
Preface page xi
Foreword by Peter J. Cameron xiii
Introduction 1
LOWELL BEINEKE, ROBIN WILSON AND PETER CAMERON
1. Graph theory 1
2. Linear algebra 10
3. Group theory 19
1 Eigenvalues of graphs 30
MICHAEL DOOB
1. Introduction 30
2. Some examples 31
3. A little matrix theory 33
4. Eigenvalues and walks 34
5. Eigenvalues and labellings of graphs 39
6. Lower bounds for the eigenvalues 43
7. Upper bounds for the eigenvalues 47
8. Other matrices related to graphs 50
9. Cospectral graphs 51
2 Graphs and matrices 56
RICHARD A. BRUALDI and BRYAN L. SHADER
1. Introduction 56
2. Some classical theorems 58
3. Digraphs 61
4. Biclique partitions of graphs 67
vn
viii Contents
5. Bipartite graphs 69
6. Permanents 72
7. Converting the permanent into the determinant 75
8. Chordal graphs and perfect Gaussian
elimination 79
9. Ranking players in tournaments 82
3 Spectral graph theory 88
DRAGOS CVETKOVIC and PETER ROWLINSON
1. Introduction 88
2. Angles 89
3. Star sets and star partitions 94
4. Star complements 96
5. Exceptional graphs 99
6. Reconstructing the characteristic polynomial 101
7. Non-complete extended/?-sums of graphs 104
8. Integral graphs 107
4 Graph Laplacians 113
BOJAN MOHAR
1. Introduction 113
2. The Laplacian of a graph 115
3. Laplace eigenvalues 117
4. Eigenvalues and vertex partitions of graphs 122
5. The max-cut problem and semi-definite
programming 125
6. Isoperimetric inequalities 127
7. The travelling salesman problem 129
8. Random walks on graphs 130
5 Automorphisms of graphs 137
PETER J. CAMERON
1. Graph automorphisms 137
2. Algorithmic aspects 139
3. Automorphisms of typical graphs 140
4. Permutation groups 141
5. Abstract groups 142
6. Cayley graphs 144
7. Vertex-transitive graphs 145
Contents ix
8. Higher symmetry 148
9. Infinite graphs 149
10. Graph homomorphisms 152
6 Cayley graphs 156
BRIAN ALSPACH
1. Introduction 156
2. Recognition 157
3. Special examples 159
4. Prevalence 160
5. Isomorphism 164
6. Enumeration 167
7. Automorphisms 168
8. Subgraphs 169
9. Hamiltonicity 171
10. Factorization 173
11. Embeddings 174
12. Applications 175
7 Finite symmetric graphs 179
CHERYL E. PRAEGER
1. Introduction 179
2. s-arc transitive graphs 181
3. Group-theoretic constructions 182
4. Quotient graphs and primitivity 186
5. Distance-transitive graphs 187
6. Local characterizations 189
7. Normal quotients 192
8. Finding automorphism groups 196
9. A geometric approach 198
10. Related families of graphs 199
8 Strongly regular graphs 203
PETER J. CAMERON
1. An example 203
2. Regularity conditions 205
3. Parameter conditions 206
4. Geometric graphs 208
5. Eigenvalues and their geometry 212
Contents
6. Rank 3 graphs 214
7. Related classes of graphs 217
9 Distance-transitive graphs 222
ARJEH M. COHEN
1. Introduction 222
2. Distance-transitivity 223
3. Graphs from groups 226
4. Combinatorial properties 230
5. Imprimitivity 233
6. Bounds 235
7. Finite simple groups 236
8. The first step 238
9. The affine case 240
10. The simple socle case 245
10 Computing with graphs and groups 250
LEONARD H. SOICHER
1. Introduction 250
2. Permutation group algorithms 251
3. Storing and accessing a S-graph 253
4. Constructing Ç7-graphs 254
5. Q-breadth-first search in a 5-graph 255
6. Automorphism groups and graph isomorphism 257
7. Computing with vertex-transitive graphs 259
8. Coset enumeration 261
9. Coset enumeration for symmetric graphs 262
Notes on contributors 267
Index of definitions 271
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| indexdate | 2024-07-09T20:05:32Z |
| institution | BVB |
| isbn | 0521801974 |
| language | English |
| lccn | 2004045915 |
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| physical | XV, 276 S. graph. Darst. |
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| series2 | Encyclopedia of mathematics and its applications |
| spelling | Topics in algebraic graph theory edited by Lowell W. Beineke... 1. publ. Cambridge [u.a.] Cambridge University Press 2004 XV, 276 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Encyclopedia of mathematics and its applications 102 "This book contains ten expository chapters written by acknowledged international experts in the field. Their well-written contributions have been carefully edited to enhance readability and to standardize the chapter structure, terminology and notation throughout the book. To help the reader, there is an extensive introductory chapter that covers the basic background material in graph theory, linear algebra and group theory. Each chapter concludes with an extensive list of references."--BOOK JACKET. Graphes, Théorie des Graph theory Graphentheorie (DE-588)4113782-6 gnd rswk-swf Algebra (DE-588)4001156-2 gnd rswk-swf Graphentheorie (DE-588)4113782-6 s Algebra (DE-588)4001156-2 s DE-604 Beineke, Lowell W. Sonstige oth Encyclopedia of mathematics and its applications 102 (DE-604)BV000903719 102 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013087957&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Topics in algebraic graph theory Encyclopedia of mathematics and its applications Graphes, Théorie des Graph theory Graphentheorie (DE-588)4113782-6 gnd Algebra (DE-588)4001156-2 gnd |
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| title | Topics in algebraic graph theory |
| title_auth | Topics in algebraic graph theory |
| title_exact_search | Topics in algebraic graph theory |
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| title_full_unstemmed | Topics in algebraic graph theory edited by Lowell W. Beineke... |
| title_short | Topics in algebraic graph theory |
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| topic | Graphes, Théorie des Graph theory Graphentheorie (DE-588)4113782-6 gnd Algebra (DE-588)4001156-2 gnd |
| topic_facet | Graphes, Théorie des Graph theory Graphentheorie Algebra |
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