An introduction to the theory of graph spectra:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge University Press
2010
|
| Schriftenreihe: | London Mathematical Society Student Texts
75 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025217057&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Includes bibliographical references (p. 333-357) and indexes |
| Umfang: | XI, 364 Seiten graph. Darst. 24 cm |
| ISBN: | 9780521118392 9780521134088 |
Internformat
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| 245 | 1 | 0 | |a An introduction to the theory of graph spectra |c Dragoš Cvetković, Mathematical Institute, Serbian Academy of Sciences and Arts, Belgrade, Peter Rowlinson, Department of Computing Science and Mathematics, University of Stirling, Scotland, Slobodan Simić, Mathematical Institute, Serbian Academy of Sciences and Arts, Belgrade |
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Datensatz im Suchindex
| _version_ | 1819280503806623744 |
|---|---|
| adam_text | Titel: An introduction to the theory of graph spectra
Autor: Cvetković, Dragoš M
Jahr: 2010
Contents
Preface page ix
1 Introduction 1
1.1 Graph spectra 1
1.2 Some more graph-theoretic notions 6
1.3 Some results from linear algebra 11
Exercises 21
Notes 23
2 Graph Operations and modifications 24
2.1 Complement, union and join of graphs 24
2.2 Coalescence and related graph compositions 29
2.3 General reduction procedures 35
2.4 Line graphs and related Operations 38
2.5 Cartesian type Operations 43
2.6 Spectra of graphs of particular types 46
Exercises 49
Notes 51
3 Spectrum and structure 52
3.1 Counting certain subgraphs 52
3.2 Regularity and bipartiteness 55
3.3 Connectedness and metric invariants 58
3.4 Line graphs and related graphs 60
3.5 More on regulär graphs 65
3.6 Strongly regulär graphs 70
3.7 Distance-regular graphs 76
3.8 Automorphisms and eigenspaces 80
3.9 Equitable partitions, divisors and main eigenvalues 83
vi Contents
3.10 Spectral bounds for graph invariants 87
3.11 Constraints on individual eigenvalues 91
Exercises 100
Notes 102
4 Characterizations by spectra 104
4.1 Spectral characterizations of certain classes of graphs 104
4.2 Cospectral graphs and the graph isomorphism
problem 118
4.3 Characterizations by eigenvalues and angles 126
Exercises 133
Notes 134
5 Structure and one eigenvalue 136
5.1 Star complements 136
5.2 Construction and characterization 141
5.3 Bounds on multiplicities 150
5.4 Graphs with least eigenvalue ?2 154
5.5 Graph foundations 155
Exercises 160
Notes 161
6 Spectral techniques 162
6.1 Decompositions of complete graphs 162
6.2 Graph homomorphisms 165
6.3 The Friendship Theorem 167
6.4 Moore graphs 169
6.5 Generalized quadrangles 172
6.6 Equiangular lines 174
6.7 Counting walks 179
Exercises 182
Notes 183
7 Laplacians 184
7.1 The Laplacian spectrum 184
7.2 The Matrix-Tree Theorem 189
7.3 The largest eigenvalue 193
7.4 Algebraic Connectivity 197
7.5 Laplacian eigenvalues and graph structure 199
7.6 Expansion 208
7.7 The normalized Laplacian matrix 212
7.8 The signless Laplacian 216
Exercises 225
Notes 226
8 Some additional results
8.1 More on graph eigenvalues
8.2 Eigenvectors and structure
8.3 Reconstructing the characteristic polynomial
8.4 Integral graphs
Exercises
Notes
9 Applications
9.1 Physics
9.2 Chemistry
9.3 Computer science
9.4 Mathematics
Notes
Contents vii
228
228
243
250
254
257
258
259
259
266
273
277
283
Appendix 285
Table AI The spectra and characteristic polynomials of the
adjacency matrix, Seidel matrix, Laplacian and
signless Laplacian for connected graphs with at most
5 vertices 286
Table A2 The eigenvalues, angles and main angles of connected
graphs with 2 to 5 vertices 290
Table A3 The spectra and characteristic polynomials of the
adjacency matrix for connected graphs with 6 vertices 294
Table A4 The spectra and characteristic polynomials of the
adjacency matrix for trees with at most 9 vertices 305
Table A5 The spectra and characteristic polynomials of the
adjacency matrix for cubic graphs with at most
12 vertices 316
References 333
Index of symbols 359
Index of terms 361
|
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| id | DE-604.BV040363256 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T16:13:27Z |
| institution | BVB |
| isbn | 9780521118392 9780521134088 |
| language | English |
| lccn | 2010287575 |
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| physical | XI, 364 Seiten graph. Darst. 24 cm |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Cambridge University Press |
| record_format | marc |
| series | London Mathematical Society Student Texts |
| series2 | London Mathematical Society Student Texts |
| spellingShingle | Cvetković, Dragoš M. 1941- An introduction to the theory of graph spectra London Mathematical Society Student Texts Graph theory Matrices |
| title | An introduction to the theory of graph spectra |
| title_auth | An introduction to the theory of graph spectra |
| title_exact_search | An introduction to the theory of graph spectra |
| title_full | An introduction to the theory of graph spectra Dragoš Cvetković, Mathematical Institute, Serbian Academy of Sciences and Arts, Belgrade, Peter Rowlinson, Department of Computing Science and Mathematics, University of Stirling, Scotland, Slobodan Simić, Mathematical Institute, Serbian Academy of Sciences and Arts, Belgrade |
| title_fullStr | An introduction to the theory of graph spectra Dragoš Cvetković, Mathematical Institute, Serbian Academy of Sciences and Arts, Belgrade, Peter Rowlinson, Department of Computing Science and Mathematics, University of Stirling, Scotland, Slobodan Simić, Mathematical Institute, Serbian Academy of Sciences and Arts, Belgrade |
| title_full_unstemmed | An introduction to the theory of graph spectra Dragoš Cvetković, Mathematical Institute, Serbian Academy of Sciences and Arts, Belgrade, Peter Rowlinson, Department of Computing Science and Mathematics, University of Stirling, Scotland, Slobodan Simić, Mathematical Institute, Serbian Academy of Sciences and Arts, Belgrade |
| title_short | An introduction to the theory of graph spectra |
| title_sort | an introduction to the theory of graph spectra |
| topic | Graph theory Matrices |
| topic_facet | Graph theory Matrices |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025217057&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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