Spectral graph theory: [CBMS Conference on Recent Advances in Spectral Graph Theory held at California State University at Fresno, June 6 - 10. 1994]
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
AMS
1997
|
| Series: | Regional conference series in mathematics
92 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 207 S. |
| ISBN: | 0821803158 |
Staff View
MARC
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| 245 | 1 | 0 | |a Spectral graph theory |b [CBMS Conference on Recent Advances in Spectral Graph Theory held at California State University at Fresno, June 6 - 10. 1994] |c Fan R. K. Chung |
| 264 | 1 | |a Providence, RI |b AMS |c 1997 | |
| 300 | |a XI, 207 S. | ||
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface
xi
Chapter
1.
Eigenvalues and the Laplacian of a graph
1
1.1.
Introduction
1
1.2.
The Laplacian and eigenvalues
2
1.3.
Basic facts about the spectrum of a graph
6
1.4.
Eigenvalues of weighted graphs
12
1.5.
Eigenvalues and random walks
14
Chapter
2.
Isoperimetric problems
23
2.1.
History
23
2.2.
The Cheeger constant of a graph
24
2.3.
The edge expansion of a graph
25
2.4.
The vertex expansion of a graph
29
2.5.
A characterization of the Cheeger constant
32
2.6.
Isoperimetric inequalities for cartesian products
35
Chapter
3.
Diameters and eigenvalues
41
3.1.
The diameter of a graph
41
3.2.
Eigenvalues and distances between two subsets
43
3.3.
Eigenvalues and distances among many subsets
46
3.4.
Eigenvalue upper bounds for manifolds
48
Chapter
4.
Paths, flows, and routing
55
viii CONTENTS
4.1.
Paths and sets of paths
55
4.2.
Flows and Cheeger constants
56
4.3.
Eigenvalues and routes with small congestion
58
4.4.
Routing in graphs
60
4.5.
Comparison theorems
64
Chapter
5.
Eigenvalues and quasi-randomness
69
5.1.
Quasi-randomness
69
5.2.
The discrepancy property
71
5.3.
The deviation of a graph
77
5.4.
Quasi-random graphs
81
Chapter
6.
Expanders and explicit constructions
87
6.1.
Probabilistic methods versus explicit constructions
87
6.2.
The expanders
88
6.3.
Examples of explicit constructions
93
6.4.
Applications of expanders in communication networks
98
6.5.
Constructions of graphs with small diameter and girth
101
6.6.
Weighted Laplacians and the
Lovász
ϋ
function
103
Chapter
7.
Eigenvalues of symmetrical graphs
109
7.1.
Symmetrical graphs
109
7.2.
Cheeger constants of symmetrical graphs
110
7.3.
Eigenvalues of symmetrical graphs
112
7.4.
Distance transitive graphs
114
7.5.
Eigenvalues and group representation theory
117
7.6.
The vibrational spectrum of a graph
119
Chapter
8.
Eigenvalues of subgraphs with boundary conditions
123
8.1.
Neumann eigenvalues and Dirichlet eigenvalues
123
CONTENTS ix
8.2.
The Neumann eigenvalues of a subgraph
124
8.3.
Neumann eigenvalues and random walks
126
8.4.
Dirichlet eigenvalues
128
8.5.
A matrix-tree theorem and Dirichlet eigenvalues
129
8.6.
Determinants and invariant field theory
131
Chapter
9.
Harnack inequalities
135
9.1.
Eigenfunctions
135
9.2.
Convex subgraphs of homogeneous graphs
136
9.3.
A Harnack inequality for homogeneous graphs
138
9.4.
Harnack inequalities for Dirichlet eigenvalues
140
9.5.
Harnack inequalities for Neumann eigenvalues
142
9.6.
Eigenvalues and diameters
144
Chapter
10.
Heat kernels
145
10.1.
The heat kernel of a graph and its induced subgraphs
145
10.2.
Basic facts on heat kernels
146
10.3.
An eigenvalue inequality
148
10.4.
Heat kernel lower bounds
150
10.5.
Matrices with given row and column sums
156
10.6.
Random walks and the heat kernel
161
Chapter
11.
Sobolev inequalities
163
11.1.
The isoperimetric dimension of a graph
163
11.2.
An isoperimetric inequality
165
11.3.
Sobolev inequalities
168
11.4.
Eigenvalue bounds
170
11.5.
Generalizations to weighted graphs and subgraphs
175
Chapter
12.
Advanced techniques for random walks on graphs
177
χ
CONTENTS
12.1.
Several approaches for bounding convergence
177
12.2.
Logarithmic Sobolev inequalities
180
12.3.
A comparison theorem for the log-Sobolev constant
185
12.4.
Logarithmic Harnack inequalities
187
12.5.
The isoperimetric dimension and the Sobolev inequality
191
Bibliography
195
Index
204
|
| any_adam_object | 1 |
| author | Chung Graham, Fan 1949- |
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| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511/.5 |
| dewey-search | 511/.5 |
| dewey-sort | 3511 15 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| genre | (DE-588)1071861417 Konferenzschrift 1994 Fresno Calif. gnd-content |
| genre_facet | Konferenzschrift 1994 Fresno Calif. |
| id | DE-604.BV011240605 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:06:23Z |
| institution | BVB |
| isbn | 0821803158 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007544339 |
| oclc_num | 312857333 |
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| physical | XI, 207 S. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | AMS |
| record_format | marc |
| series | Regional conference series in mathematics |
| series2 | Regional conference series in mathematics |
| spelling | Chung Graham, Fan 1949- Verfasser (DE-588)112177042 aut Spectral graph theory [CBMS Conference on Recent Advances in Spectral Graph Theory held at California State University at Fresno, June 6 - 10. 1994] Fan R. K. Chung Providence, RI AMS 1997 XI, 207 S. txt rdacontent n rdamedia nc rdacarrier Regional conference series in mathematics 92 Graphentheorie (DE-588)4113782-6 gnd rswk-swf Spektrum Mathematik (DE-588)4182180-4 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 1994 Fresno Calif. gnd-content Graphentheorie (DE-588)4113782-6 s Spektrum Mathematik (DE-588)4182180-4 s DE-604 Regional conference series in mathematics 92 (DE-604)BV000004346 92 Digitalisierung TU Muenchen application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007544339&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Chung Graham, Fan 1949- Spectral graph theory [CBMS Conference on Recent Advances in Spectral Graph Theory held at California State University at Fresno, June 6 - 10. 1994] Regional conference series in mathematics Graphentheorie (DE-588)4113782-6 gnd Spektrum Mathematik (DE-588)4182180-4 gnd |
| subject_GND | (DE-588)4113782-6 (DE-588)4182180-4 (DE-588)1071861417 |
| title | Spectral graph theory [CBMS Conference on Recent Advances in Spectral Graph Theory held at California State University at Fresno, June 6 - 10. 1994] |
| title_auth | Spectral graph theory [CBMS Conference on Recent Advances in Spectral Graph Theory held at California State University at Fresno, June 6 - 10. 1994] |
| title_exact_search | Spectral graph theory [CBMS Conference on Recent Advances in Spectral Graph Theory held at California State University at Fresno, June 6 - 10. 1994] |
| title_full | Spectral graph theory [CBMS Conference on Recent Advances in Spectral Graph Theory held at California State University at Fresno, June 6 - 10. 1994] Fan R. K. Chung |
| title_fullStr | Spectral graph theory [CBMS Conference on Recent Advances in Spectral Graph Theory held at California State University at Fresno, June 6 - 10. 1994] Fan R. K. Chung |
| title_full_unstemmed | Spectral graph theory [CBMS Conference on Recent Advances in Spectral Graph Theory held at California State University at Fresno, June 6 - 10. 1994] Fan R. K. Chung |
| title_short | Spectral graph theory |
| title_sort | spectral graph theory cbms conference on recent advances in spectral graph theory held at california state university at fresno june 6 10 1994 |
| title_sub | [CBMS Conference on Recent Advances in Spectral Graph Theory held at California State University at Fresno, June 6 - 10. 1994] |
| topic | Graphentheorie (DE-588)4113782-6 gnd Spektrum Mathematik (DE-588)4182180-4 gnd |
| topic_facet | Graphentheorie Spektrum Mathematik Konferenzschrift 1994 Fresno Calif. |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007544339&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000004346 |
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