Graphs and matrices:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London [u.a.]
Springer [u.a.]
2010
|
| Series: | Universitext
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 171 Seiten graph. Darst. |
| ISBN: | 9781848829800 |
Staff View
MARC
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| 100 | 1 | |a Bapat, Ravi B. |e Verfasser |0 (DE-588)115635831 |4 aut | |
| 245 | 1 | 0 | |a Graphs and matrices |c R. B. Bapat |
| 264 | 1 | |a London [u.a.] |b Springer [u.a.] |c 2010 | |
| 300 | |a IX, 171 Seiten |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface
............................................................
v
1
Preliminaries
.................................................. 1
1.1
Matrices
.................................................. 1
1.2
Eigenvalues of symmetric matrices
............................ 5
1.3
Generalized inverses
........................................ 7
1.4
Graphs
................................................... 9
2
Incidence Matrix
............................................... 11
2.1
Rank
..................................................... 12
2.2
Minors
................................................... 13
2.3
Path matrix
................................................ 15
2.4
Integer generalized inverses
.................................. 16
2.5
Moore-Penrose inverse
...................................... 17
2.6 0-1
Incidence matrix
...................................... 19
2.7
Matchings in bipartite graphs
................................. 21
3
Adjacency Matrix
.............................................. 25
3.1
Eigenvalues of some graphs
.................................. 26
3.2
Determinant
............................................... 28
3.3
Bounds
................................................... 31
3.4
Energy of a graph
.......................................... 36
3.5
Antiadjacency matrix of a directed graph
....................... 37
3.6
Nonsingular trees
........................................... 39
4
Laplacian Matrix
.............................................. 45
4.1
Basic properties
............................................ 46
4.2
Computing Laplacian eigenvalues
............................. 47
4.3
Matrix-tree theorem
........................................ 48
4.4
Bounds for Laplacian spectral radius
.......................... 50
4.5
Edge-Laplacian of a tree
.................................... 51
viii Contents
5
Cycles
and Cuts
................................................ 57
5.1
Fundamental cycles and fundamental cuts
...................... 57
5.2
Fundamental matrices
....................................... 59
5.3
Minors
................................................... 60
6
Regular Graphs
................................................ 65
6.1
Perron-Frobenius theory
.................................... 65
6.2
Adjacency algebra of a regular graph
.......................... 70
6.3
Complement and line graph of a regular graph
.................. 70
6.4
Strongly regular graphs and friendship theorem
................. 73
6.5
Graphs with maximum energy
................................ 76
7
Algebraic Connectivity
......................................... 81
7.1
Preliminary results
......................................... 81
7.2
Classification of trees
....................................... 83
7.3
Monotonicity properties of Fiedler vector
...................... 88
7.4
Bounds for algebraic connectivity
............................. 89
8
Distance Matrix of a Tree
....................................... 95
8.1
Distance matrix of a graph
................................... 96
8.2
Distance matrix and Laplacian of a tree
........................ 99
8.3
Eigenvalues of the distance matrix of a tree
.....................104
9
Resistance Distance
............................................
Ill
9.1
The triangle inequality
......................................112
9.2
Network flows
.............................................113
9.3
A random walk on graphs
....................................116
9.4
Effective resistance in electrical networks
......................118
9.5
Resistance matrix
..........................................119
10
Laplacian Eigenvalues of Threshold Graphs
.......................125
10.1
Majorization
...............................................125
10.2
Threshold graphs
...........................................129
10.3
Spectral integral variation
....................................131
11
Positive Definite Completion Problem
............................137
11.1
Nonsingular completion
.....................................137
11.2
Chordal graphs
.............................................138
11.3
Positive definite completion
..................................140
12
Matrix Games Based on Graphs
.................................145
12.1
Matrix games
..............................................145
12.2
Vertex selection games
......................................147
12.3
Tournament games
.........................................148
12.4
Incidence matrix games
.....................................151
Contents ix
Hints and Solutions to Selected Exercises
..............................159
Bibliography
.......................................................165
Index
.............................................................169
|
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| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.5 |
| dewey-search | 511.5 |
| dewey-sort | 3511.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV035843977 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:05:56Z |
| institution | BVB |
| isbn | 9781848829800 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018702218 |
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| owner_facet | DE-20 DE-703 DE-91 DE-BY-TUM DE-11 DE-188 DE-824 |
| physical | IX, 171 Seiten graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Springer [u.a.] |
| record_format | marc |
| series2 | Universitext |
| spelling | Bapat, Ravi B. Verfasser (DE-588)115635831 aut Graphs and matrices R. B. Bapat London [u.a.] Springer [u.a.] 2010 IX, 171 Seiten graph. Darst. txt rdacontent n rdamedia nc rdacarrier Universitext Graph theory Matrices Graphentheorie (DE-588)4113782-6 gnd rswk-swf Graphentheorie (DE-588)4113782-6 s DE-604 Erscheint auch als Online-Ausgabe 978-1-84882-981-7 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018702218&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bapat, Ravi B. Graphs and matrices Graph theory Matrices Graphentheorie (DE-588)4113782-6 gnd |
| subject_GND | (DE-588)4113782-6 |
| title | Graphs and matrices |
| title_auth | Graphs and matrices |
| title_exact_search | Graphs and matrices |
| title_full | Graphs and matrices R. B. Bapat |
| title_fullStr | Graphs and matrices R. B. Bapat |
| title_full_unstemmed | Graphs and matrices R. B. Bapat |
| title_short | Graphs and matrices |
| title_sort | graphs and matrices |
| topic | Graph theory Matrices Graphentheorie (DE-588)4113782-6 gnd |
| topic_facet | Graph theory Matrices Graphentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018702218&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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