Spectra of graphs: theory and applications
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
Heidelberg ; Leipzig
Barth
1995
|
| Ausgabe: | 3., rev. and enl. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturangaben |
| Beschreibung: | 447 S. graph. Darst. |
| ISBN: | 3335004078 |
Internformat
MARC
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| 100 | 1 | |a Cvetković, Dragoš M. |d 1941- |e Verfasser |0 (DE-588)110230485 |4 aut | |
| 245 | 1 | 0 | |a Spectra of graphs |b theory and applications |c by Dragoš M. Cvetković, Michael Doob and Horst Sachs |
| 250 | |a 3., rev. and enl. ed. | ||
| 264 | 1 | |a Heidelberg ; Leipzig |b Barth |c 1995 | |
| 300 | |a 447 S. |b graph. Darst. | ||
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Datensatz im Suchindex
| _version_ | 1804124205915045888 |
|---|---|
| adam_text | SPECTR
A OF GRAPH
S
THEOR
Y AND APPLICATIONS
BY DRAGOS M. CVETKOVIC, MICHAEL DOOB
AND HORST SACHS
3RD REVISED AND ENLARGED EDITION
WITH 51 FIGURES AND 12 TABLES
JOHANN AMBROSIUS BART
H VERLAG
HEIDELBERG YY LEIPZIG
CONTENT
S
0
. INTRODUCTIO
N 1
1
0.1
. WHA
T TH
E SPECTRU
M OF A GRAP
H IS AN
D HOW I
T IS PIESENTE
D IN THI
S BOO
K ...
. 11
0.2. SOM
E MOI
E GRAP
H THEORETI
C NOTION
S AN
D CONVENTIONS 14
0.3
. SOM
E THEOREM
S FROM MATRI
X THEOR
Y AN
D THEI
R APPLICATIO
N T
O TH
E SPECTRU
M OF
A GRAP
H 17
1
. BASI
C PROPERTIE
S O
F TH
E SPECTRU
M O
F A GRAP
H 2
3
1.1. TH
E ADJACENC
Y MATRI
X AN
D TH
E (ORDINARY
) SPECTRU
M OF A GRAP
H 23
1.2. A GENERA
L METHO
D FOR DEFINING DIFFERENT KIND
S OF GRAP
H SPECTR
A 24
1.3. SOM
E REMARK
S CONCERNIN
G CURREN
T SPECTR
A 28
1.4. TH
E COEFFICIENTS OF P
G
(A
) 31
1.5. TH
E COEFFICIENTS OF C
G
(A
) 37
1.6. TH
E COEFFICIENTS OF QG(A
) 40
1.7. A FORMUL
A CONNECTIN
G TH
E CYCLIC STRUCTUR
E AN
D TH
E TRE
E STRUCTUR
E OF A REGULAE
R
OR SEMIREGULA
R MULTIGRAP
H 4
1
1.8. O
N TH
E NUMBE
R OF WALKS 43
1.9. MISCELLANEOU
S RESULT
S AN
D PROBLEM
S 47
2
. OPERATION
S O
N GRAPH
S AN
D TH
E RESULTIN
G SPECTR
A 5
1
2.1
. TH
E POLYNOMIA
L OF A GRAP
H 51
2.2
. TH
E SPECTRU
M OF TH
E COMPLEMENT
, DIREC
T SUM
, AN
D COMPLET
E PRODUC
T OF GRAPH
S 54
2.3
. REDUCTIO
N PROCEDURE
S FOR CALCULATIN
G TH
E CHARACTERISTI
C POLYNOMIA
L 59
2.4. LINE GRAPH
S AN
D TOTA
L GRAPH
S 61
2.5
. NEP
S AN
D BOOLEA
N FUNCTION
S 65
2.6. TH
E DETEIMINATIO
N OF CHARACTERISTI
C POLYNOMIAL
S AN
D SPECTR
A OF GIAPH
S OF
SOM
E PARTICULA
R TYPE
S 72
2.7
. MISCELLANEOU
S RESULT
S AN
D PROBLEM
S 77
3
. RELATION
S BETWEE
N SPECTRA
L AN
D STRUCTURA
L PROPERTIE
S O
F GRAPH
S . 8
0
3.1
. DIGRAPH
S 80
3.2. GRAPH
S 84
3.3
. REGULAE
R GRAPH
S 94
3.4. SOM
E REMARK
S ON STIONGL
Y REGULA
I GIAPH
S 103
3.5
. EIGENVECTOI
S 104
8 CONTENT
S
3.6. MISCELLANEOUS RESULT
S AN
D PROBLEM
S 112
4
. TH
E DIVISO
R O
F A GRAP
H 11
6
4.1
. TH
E DIVISOR CONCEP
T 116
4.2. DIVISOR AN
D COVER 117
4.3
. A GENEIALIZATIO
N OF TH
E DIVISO
I CONCEP
T 118
4.4. SYMMETR
Y PROPERTIE
S AN
D DIVISOR
S OF GRAPH
S 118
4.5
. TH
E FUNDAMENTA
L LEMM
A CONNECTIN
G TH
E DIVISOR AN
D TH
E SPECTRU
M 121
4.6. TH
E DIVISO
R - A
N EFFECTIVE TOO
L FOR FACTORIN
G TH
E CHARACTERISTI
C POLYNOMIA
L . . 125
4.7. TH
E DIVISOR - A MEDIATO
R BETWEE
N STRUCTUR
E AN
D SPECTRU
M 128
4.8. MISCELLANEOU
S RESULT
S AN
D PROBLEM
S 131
5
. TH
E SPECTRU
M AN
D TH
E GROU
P O
F AUTOMORPHISM
S 13
4
5.1
. SYMMETR
Y AN
D SIMPL
E EIGENVALUES 134
5.2. TH
E SPECTRU
M AN
D REPRESENTATION
S OF TH
E AUTOMOIPHIS
M GROU
P 141
5.3. TH
E FRON
T DIVISO
R INDUCE
D BY A SUBGROU
P OF TH
E AUTOMORPHIS
M GIOU
P 149
5.4. COSPECTIA
L GIAPH
S WIT
H PRESCRIBE
D (DISTINCT
) AUTOMOIPHIS
M GROUP
S 153
5.5. MISCELLANEOU
S RESULT
S AN
D PROBLEM
S 153
6
. CHARACTERIZATIO
N O
F GRAPH
S B
Y MEAN
S O
F SPECTR
A 15
6
6.1
. SOM
E FAMILIES OF NON-ISOMORPHI
C COSPECTRA
L GRAPH
S 156
6.2. TH
E CHARACTERIZATIO
N OF A GRAP
H BY IT
S SPECTRU
M 161
6.3. TH
E CHARACTERIZATIO
N AN
D OTHE
R SPECTRA
L PROPEITIE
S OF LIN
E GRAPH
S 168
6.4. METRICALL
Y REGULAE
R GRAPH
S 178
6.5. TH
E (-1
, L,0)-ADJACENC
Y MATRI
X AN
D SEIDEL SWITCHIN
G 183
6.6. MISCELLANEOU
S RESULT
S AN
D PROBLEM
S 185
7
. SPECTRA
L TECHNIQUE
S I
N GRAP
H THEOR
Y AN
D COMBINATORIC
S 18
9
7.1
. TH
E EXISTENC
E AN
D TH
E NON-EXISTENC
E OF CERTAI
N COMBINATORIA
L OBJECT
S 189
7.2. STRONGL
Y REGULAE
R GRAPH
S AN
D DISTANCE-TRANSITIV
E GRAPH
S 193
7.3. EQUIANGULA
R LINE
S AN
D TWO-GRAPH
S 199
7.4. CONNECTEDNES
S AN
D BIPARTITENES
S OF CERTAI
N GRAP
H PRODUCT
S 203
7.5. DETERMINATIO
N OF TH
E NUMBE
R OF WALKS 209
7.6. DETERMIANTIO
N OF TH
E NUMBE
R OF SPANNIN
G TREE
S 217
7.7. EXTERNA
L PROBLEM
S 221
7.8. MISCELLANEOU
S RESULT
S AN
D PROBLEM
S 223
8
. APPLICATION
S I
N CHEMISTR
Y AN
D PHYSIC
S 22
8
8.1
. HUECKEL
S THEOR
Y 228
8.2. GRAPH
S RELATE
D T
O BENZENOI
D HYDROCARBON
S 239
8.3
. TH
E DIME
R PROBLE
M 245
8.4. VIBRATIO
N OF A MEMBRAN
E 252
8.5. MISCELLANEOU
S RESULT
S AN
D PROBLEM
S 258
9
. SOM
E ADDITIONA
L RESULT
S 26
0
9.1
. EIGENVALUE
S AN
D IMBEDDING
S 260
9.2. TH
E DISTANC
E POLYNOMIA
L 263
CONTENT
S 9
9.3
. TH
E ALGEBRAI
C CONNECTIVITY OF A GRAP
H 265
9.4. INTEGRA
L GRAPH
S 266
9.5. SOM
E PROBLEM
S 266
APPENDIX
. TABLE
S O
F GRAP
H SPECTR
A 26
8
BIBLIOGRAPH
Y 32
4
INDE
X O
F SYMBOL
S 36
0
INDE
X O
F NAME
S 36
1
SUBJEC
T INDE
X 36
4
APPENDI
X A
.
COMMENT
S O
N TH
E FIRS
T TW
O EDITION
S O
F TH
E BOO
K 36
9
APPENDI
X B
.
RECEN
T DEVELOPMENT
S I
N TH
E THEOR
Y O
F GRAP
H SPECTR
A 37
3
B.
L A SURVE
Y OF RELEVAN
T BOOK
S 373
B.2 EXPOSITOR
Y PAPER
S 376
B.3 GRAPH
S WIT
H LEAS
T EIGENVALUE -
2 378
B.4 LARGES
T EIGENVALUE 381
B.5 SECOND LARGES
T EIGENVALUE 392
B.6 DISTANCE-REGULA
R GRAPH
S 394
B.6.1 STRONGL
Y REGULAE
R GRAPH
S 395
B.6.2 OTHE
R DISTANCE-REGULA
R GRAPH
S 396
B.7 GRAP
H ANGLE
S AN
D STA
R PARTITION
S 396
B.7.1 EXAMPLE
S AN
D INTRODUCIN
G COMMENT
S 397
B.7.2 SOME PROPERTIE
S OF GRAP
H ANGLE
S 399
B.7.3 MAI
N ANGLES 402
B.7.4 EA-RECONSTRUCTIO
N OF TREE
S 404
B.7.5 ULAM
S RECONSTRUCTIO
N CONJECTUR
E FOR GRAPH
S 405
B.7.6 STA
R PARTITION
S AN
D CANONICA
L STA
R BASE
S 407
B.8 GRAP
H LAPLACIAN
S 409
B.9 TABLE
S OF GRAP
H SPECTR
A 411
B.10 TH
E EXPER
T SYSTEM GRAP
H AN
D TH
E COMPUTER PROGRA
M GRAFFIT
I 413
B.10.1 SYSTE
M GRAP
H 414
B.10.2 PROGRA
M GRAFFIT
I 416
B.L
L GRAP
H SPECTR
A AN
D COMBINATORIA
L OPTIMIZATIO
N 417
B.12 MISCELLANEOU
S RESULT
S 418
ADDITIONA
L BIBLIOGRAPH
Y 42
7
|
| any_adam_object | 1 |
| author | Cvetković, Dragoš M. 1941- Doob, Michael Sachs, Horst |
| author_GND | (DE-588)110230485 |
| author_facet | Cvetković, Dragoš M. 1941- Doob, Michael Sachs, Horst |
| author_role | aut aut aut |
| author_sort | Cvetković, Dragoš M. 1941- |
| author_variant | d m c dm dmc m d md h s hs |
| building | Verbundindex |
| bvnumber | BV009850955 |
| callnumber-first | Q - Science |
| callnumber-label | QA166 |
| callnumber-raw | QA166 |
| callnumber-search | QA166 |
| callnumber-sort | QA 3166 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 890 |
| ctrlnum | (OCoLC)41278595 (DE-599)BVBBV009850955 |
| dewey-full | 511/.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| 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 |
| edition | 3., rev. and enl. ed. |
| format | Book |
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| id | DE-604.BV009850955 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:41:58Z |
| institution | BVB |
| isbn | 3335004078 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006521229 |
| oclc_num | 41278595 |
| open_access_boolean | |
| owner | DE-12 DE-634 |
| owner_facet | DE-12 DE-634 |
| physical | 447 S. graph. Darst. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Barth |
| record_format | marc |
| spelling | Cvetković, Dragoš M. 1941- Verfasser (DE-588)110230485 aut Spectra of graphs theory and applications by Dragoš M. Cvetković, Michael Doob and Horst Sachs 3., rev. and enl. ed. Heidelberg ; Leipzig Barth 1995 447 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturangaben Graph theory Matrices Graph (DE-588)4021842-9 gnd rswk-swf Spektrum Mathematik (DE-588)4182180-4 gnd rswk-swf Graphentheorie (DE-588)4113782-6 gnd rswk-swf Eigenwert (DE-588)4151200-5 gnd rswk-swf Spektrum (DE-588)4056139-2 gnd rswk-swf Graph (DE-588)4021842-9 s Spektrum (DE-588)4056139-2 s 1\p DE-604 Eigenwert (DE-588)4151200-5 s Graphentheorie (DE-588)4113782-6 s 2\p DE-604 Spektrum Mathematik (DE-588)4182180-4 s 3\p DE-604 Doob, Michael Verfasser aut Sachs, Horst Verfasser aut DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006521229&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Cvetković, Dragoš M. 1941- Doob, Michael Sachs, Horst Spectra of graphs theory and applications Graph theory Matrices Graph (DE-588)4021842-9 gnd Spektrum Mathematik (DE-588)4182180-4 gnd Graphentheorie (DE-588)4113782-6 gnd Eigenwert (DE-588)4151200-5 gnd Spektrum (DE-588)4056139-2 gnd |
| subject_GND | (DE-588)4021842-9 (DE-588)4182180-4 (DE-588)4113782-6 (DE-588)4151200-5 (DE-588)4056139-2 |
| title | Spectra of graphs theory and applications |
| title_auth | Spectra of graphs theory and applications |
| title_exact_search | Spectra of graphs theory and applications |
| title_full | Spectra of graphs theory and applications by Dragoš M. Cvetković, Michael Doob and Horst Sachs |
| title_fullStr | Spectra of graphs theory and applications by Dragoš M. Cvetković, Michael Doob and Horst Sachs |
| title_full_unstemmed | Spectra of graphs theory and applications by Dragoš M. Cvetković, Michael Doob and Horst Sachs |
| title_short | Spectra of graphs |
| title_sort | spectra of graphs theory and applications |
| title_sub | theory and applications |
| topic | Graph theory Matrices Graph (DE-588)4021842-9 gnd Spektrum Mathematik (DE-588)4182180-4 gnd Graphentheorie (DE-588)4113782-6 gnd Eigenwert (DE-588)4151200-5 gnd Spektrum (DE-588)4056139-2 gnd |
| topic_facet | Graph theory Matrices Graph Spektrum Mathematik Graphentheorie Eigenwert Spektrum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006521229&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT cvetkovicdragosm spectraofgraphstheoryandapplications AT doobmichael spectraofgraphstheoryandapplications AT sachshorst spectraofgraphstheoryandapplications |