Inequalities for graph eigenvalues:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge Univ. Press
2015
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | London Mathematical Society lecture note series
423 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 298 S. graph. Darst. |
| ISBN: | 9781107545977 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV042733736 | ||
| 003 | DE-604 | ||
| 005 | 20150826 | ||
| 007 | t | ||
| 008 | 150804s2015 d||| |||| 00||| eng d | ||
| 020 | |a 9781107545977 |9 978-1-107-54597-7 | ||
| 024 | 3 | |a 9781107545977 | |
| 035 | |a (OCoLC)915841008 | ||
| 035 | |a (DE-599)BSZ443071446 | ||
| 040 | |a DE-604 |b ger | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-91G |a DE-19 | ||
| 082 | 0 | |a 512.9/436 | |
| 084 | |a SI 320 |0 (DE-625)143123: |2 rvk | ||
| 084 | |a MAT 055f |2 stub | ||
| 084 | |a MAT 152f |2 stub | ||
| 100 | 1 | |a Stanić, Zoran |d 1975- |e Verfasser |0 (DE-588)1074890655 |4 aut | |
| 245 | 1 | 0 | |a Inequalities for graph eigenvalues |c Zoran Stanić |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge |b Cambridge Univ. Press |c 2015 | |
| 300 | |a XI, 298 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a London Mathematical Society lecture note series |v 423 | |
| 650 | 0 | 7 | |a Ungleichung |0 (DE-588)4139098-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Spektrum |g Mathematik |0 (DE-588)4182180-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Graphentheorie |0 (DE-588)4113782-6 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Graphentheorie |0 (DE-588)4113782-6 |D s |
| 689 | 0 | 1 | |a Spektrum |g Mathematik |0 (DE-588)4182180-4 |D s |
| 689 | 0 | 2 | |a Ungleichung |0 (DE-588)4139098-2 |D s |
| 689 | 0 | |5 DE-604 | |
| 830 | 0 | |a London Mathematical Society lecture note series |v 423 |w (DE-604)BV000000130 |9 423 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028164708&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-028164708 | ||
Datensatz im Suchindex
| _version_ | 1804174947312992256 |
|---|---|
| adam_text | Titel: Inequalities for graph eigenvalues
Autor: Stanić, Zoran
Jahr: 2015
Contents
Preface page ix
1 Introduction 1
1.1 Graph-theoretic notions 1
1.1.1 Some graphs 5
1.2 Spectra of graphs 8
1.2.1 Spectrum of a graph 10
1.2.2 Laplacian spectrum of a graph 12
1.2.3 Signless Laplacian spectrum of a graph 14
1.2.4 Relations between A,L, and Q 16
1.3 Some more specific elements of the theory of graph
spectra 18
1.3.1 Eigenvalue interlacing 18
1.3.2 Small perturbations 19
1.3.3 Hoffman program 20
1.3.4 Star complement technique 21
1.4 A few more words 22
1.4.1 Selected applications 22
1.4.2 Spectral inequalities and extremal graph theory 26
1.4.3 Computer help 27
2 Spectral radius 28
2.1 General inequalities 28
2.1.1 Walks in graphs 29
2.1.2 Graph diameter 38
2.1.3 Other inequalities 43
2.2 Inequalities for spectral radius of particular types of graph 50
2.2.1 Bipartite graphs 51
2.2.2 Forbidden induced subgraphs 55
V
vi
Contents
2.2.3 Nearly regular graphs
2.2.4 Nested graphs
2.3 Extremal graphs
2.3.1 Graphs whose spectral radius does not exceed
3¿2
2
2.3.2 Order, size, and maximal spectral radius
2.3.3 Diameter and extremal spectral radius
2.3.4 Trees
2.3.5 Various results
2.3.6 Ordering graphs
Exercises
Notes
3 Least eigenvalue
3.1 Inequalities
3.1.1 Bounds in terms of order and size
3.1.2 Inequalities in terms of clique number, inde-
pendence number or chromatic number
3.2 Graphs whose least eigenvalue is at least —2
3.3 Graphs with minimal least eigenvalue
3.3.1 Least eigenvalue under small graph perturbations
3.3.2 Graphs of fixed order and size
3.3.3 Graphs with prescribed properties
Exercises
Notes
4 Second largest eigenvalue
4.1 Inequalities
4.1.1 Regular graphs
4.1.2 Trees
4.2 Graphs with small second largest eigenvalue
4.2.1 Graphs with %% j or hi y/l - 1
4.2.2 The golden section bound
4.2.3 Graphs whose second largest eigenvalue does
not exceed 1
4.2.4 Trees with kx ¡2
4.2.5 Notes on reflexive cacti
4.2.6 Regular graphs
4.3 Appendix
Exercises
Notes
56
58
63
63
66
68
71
74
76
82
85
87
87
88
90
92
95
96
98
100
102
103
105
105
106
113
115
115
117
118
123
125
126
134
143
144
Contents vii
5 Other eigenvalues of the adjacency matrix 146
5.1 Bounds for A,- 146
5.2 Graphs with A3 0 149
5.3 Graphs G with A„_i(G) and A„_i(G) —1 150
Exercises 153
Notes 154
6 Laplacian eigenvalues 155
6.1 General inequalities for ¿-spectral radius 155
6.1.1 Upper bounds 156
6.1.2 Lower bounds 161
6.2 Bounding ¿-spectral radius of particular types of graph 163
6.2.1 Triangle-free graphs 163
6.2.2 Triangulation graphs 165
6.2.3 Bipartite graphs and trees 167
6.3 Graphs with small ¿-spectral radius 168
6.4 Graphs with maximal ¿-spectral radius 169
6.4.1 Graphs with ß 1 = n 169
6.4.2 Various graphs 171
6.5 Ordering graphs by ¿-spectral radius 174
6.6 General inequalities for algebraic connectivity 176
6.6.1 Upper and lower bounds 179
6.6.2 Bounding graph invariants by algebraic con-
nectivity 184
6.6.3 Isoperimetric problem and graph expansion 185
6.7 Notes on algebraic connectivity of trees 188
6.8 Graphs with extremal algebraic connectivity 190
6.9 Ordering graphs by algebraic connectivity 193
6.10 Other ¿-eigenvalues 193
6.10.1 Bounds for /1¡ 194
6.10.2 Graphs with small ß2 or ¿I3 197
Exercises 198
Notes 202
7 Signless Laplacian eigenvalues 204
7.1 General inequalities for ß-spectral radius 204
7.1.1 Transferring upper bounds for 205
7.2 Bounds for ß-spectral radius of connected nested graphs 210
7.3 Graphs with small 2-spectral radius 213
7.4 Graphs with maximal Ö-spectral radius 214
7.4.1 Order, size, and maximal Q-spectral radius 214
viii
Contents
7.4.2 Other results 216
7.5 Ordering graphs by g-spectral radius 217
7.6 Least g-eigenvalue 217
7.6.1 Upper and lower bounds 218
7.6.2 Small graph perturbations and graphs with
extremal least g-eigenvalue 221
7.7 Other g-eigenvalues 222
Exercises 227
Notes 229
8 Inequalities for multiple eigenvalues 231
8.1 Spectral spread 231
8.1.1 Upper and lower bounds 231
8.1.2 g-Spread and ¿-spread 234
8.1.3 Extremal graphs 234
8.2 Spectral gap 236
8.3 Inequalities of Nordhaus-Gaddum type 238
8.4 Other inequalities that include two eigenvalues 240
8.5 Graph energy 243
8.6 Estrada index 245
Exercises 247
Notes 250
9 Other spectra of graphs 251
9.1 Normalized ¿-eigenvalues 251
9.1.1 Upper and lower bounds for pj and i 253
9.2 Seidel matrix eigenvalues 255
9.3 Distance matrix eigenvalues 255
9.3.1 Upper and lower bounds for 257
9.3.2 Graphs with small ¿2 or large Sn 260
Exercises 261
Notes 262
References 265
Inequalities 290
Index 294
|
| any_adam_object | 1 |
| author | Stanić, Zoran 1975- |
| author_GND | (DE-588)1074890655 |
| author_facet | Stanić, Zoran 1975- |
| author_role | aut |
| author_sort | Stanić, Zoran 1975- |
| author_variant | z s zs |
| building | Verbundindex |
| bvnumber | BV042733736 |
| classification_rvk | SI 320 |
| classification_tum | MAT 055f MAT 152f |
| ctrlnum | (OCoLC)915841008 (DE-599)BSZ443071446 |
| dewey-full | 512.9/436 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.9/436 |
| dewey-search | 512.9/436 |
| dewey-sort | 3512.9 3436 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01723nam a2200445 cb4500</leader><controlfield tag="001">BV042733736</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20150826 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">150804s2015 d||| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781107545977</subfield><subfield code="9">978-1-107-54597-7</subfield></datafield><datafield tag="024" ind1="3" ind2=" "><subfield code="a">9781107545977</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)915841008</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BSZ443071446</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-91G</subfield><subfield code="a">DE-19</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">512.9/436</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SI 320</subfield><subfield code="0">(DE-625)143123:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 055f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 152f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Stanić, Zoran</subfield><subfield code="d">1975-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)1074890655</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Inequalities for graph eigenvalues</subfield><subfield code="c">Zoran Stanić</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">1. publ.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Cambridge</subfield><subfield code="b">Cambridge Univ. Press</subfield><subfield code="c">2015</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XI, 298 S.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">London Mathematical Society lecture note series</subfield><subfield code="v">423</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Ungleichung</subfield><subfield code="0">(DE-588)4139098-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Spektrum</subfield><subfield code="g">Mathematik</subfield><subfield code="0">(DE-588)4182180-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Graphentheorie</subfield><subfield code="0">(DE-588)4113782-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Graphentheorie</subfield><subfield code="0">(DE-588)4113782-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Spektrum</subfield><subfield code="g">Mathematik</subfield><subfield code="0">(DE-588)4182180-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Ungleichung</subfield><subfield code="0">(DE-588)4139098-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">London Mathematical Society lecture note series</subfield><subfield code="v">423</subfield><subfield code="w">(DE-604)BV000000130</subfield><subfield code="9">423</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028164708&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-028164708</subfield></datafield></record></collection> |
| id | DE-604.BV042733736 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T07:08:29Z |
| institution | BVB |
| isbn | 9781107545977 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028164708 |
| oclc_num | 915841008 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-19 DE-BY-UBM |
| owner_facet | DE-91G DE-BY-TUM DE-19 DE-BY-UBM |
| physical | XI, 298 S. graph. Darst. |
| publishDate | 2015 |
| publishDateSearch | 2015 |
| publishDateSort | 2015 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | London Mathematical Society lecture note series |
| series2 | London Mathematical Society lecture note series |
| spelling | Stanić, Zoran 1975- Verfasser (DE-588)1074890655 aut Inequalities for graph eigenvalues Zoran Stanić 1. publ. Cambridge Cambridge Univ. Press 2015 XI, 298 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier London Mathematical Society lecture note series 423 Ungleichung (DE-588)4139098-2 gnd rswk-swf Spektrum Mathematik (DE-588)4182180-4 gnd rswk-swf Graphentheorie (DE-588)4113782-6 gnd rswk-swf Graphentheorie (DE-588)4113782-6 s Spektrum Mathematik (DE-588)4182180-4 s Ungleichung (DE-588)4139098-2 s DE-604 London Mathematical Society lecture note series 423 (DE-604)BV000000130 423 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028164708&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Stanić, Zoran 1975- Inequalities for graph eigenvalues London Mathematical Society lecture note series Ungleichung (DE-588)4139098-2 gnd Spektrum Mathematik (DE-588)4182180-4 gnd Graphentheorie (DE-588)4113782-6 gnd |
| subject_GND | (DE-588)4139098-2 (DE-588)4182180-4 (DE-588)4113782-6 |
| title | Inequalities for graph eigenvalues |
| title_auth | Inequalities for graph eigenvalues |
| title_exact_search | Inequalities for graph eigenvalues |
| title_full | Inequalities for graph eigenvalues Zoran Stanić |
| title_fullStr | Inequalities for graph eigenvalues Zoran Stanić |
| title_full_unstemmed | Inequalities for graph eigenvalues Zoran Stanić |
| title_short | Inequalities for graph eigenvalues |
| title_sort | inequalities for graph eigenvalues |
| topic | Ungleichung (DE-588)4139098-2 gnd Spektrum Mathematik (DE-588)4182180-4 gnd Graphentheorie (DE-588)4113782-6 gnd |
| topic_facet | Ungleichung Spektrum Mathematik Graphentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028164708&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000130 |
| work_keys_str_mv | AT staniczoran inequalitiesforgrapheigenvalues |