Algebraic graph theory: morphisms, monoids and matrices
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin/Boston
De Gruyter
[2019]
|
| Edition: | 2nd edition |
| Series: | De Gruyter studies in mathematics
Volume 41 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Physical Description: | XVIII, 329 Seiten Illustrationen, Diagramme |
| ISBN: | 9783110616125 |
Staff View
MARC
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| 016 | 7 | |a 1175757470 |2 DE-101 | |
| 020 | |a 9783110616125 |c hardcover |9 978-3-11-061612-5 | ||
| 035 | |a (OCoLC)1083224665 | ||
| 035 | |a (DE-599)DNB1175757470 | ||
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| 100 | 1 | |a Knauer, Ulrich |d 1942- |e Verfasser |0 (DE-588)14404787X |4 aut | |
| 245 | 1 | 0 | |a Algebraic graph theory |b morphisms, monoids and matrices |c Ulrich Knauer and Kolja Knauer |
| 250 | |a 2nd edition | ||
| 264 | 1 | |a Berlin/Boston |b De Gruyter |c [2019] | |
| 264 | 4 | |c © 2019 | |
| 300 | |a XVIII, 329 Seiten |b Illustrationen, Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a De Gruyter studies in mathematics |v Volume 41 | |
| 650 | 0 | 7 | |a Algebra |0 (DE-588)4001156-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Graphentheorie |0 (DE-588)4113782-6 |2 gnd |9 rswk-swf |
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| 653 | |a Fachpublikum/ Wissenschaft | ||
| 653 | |a MAT002000 | ||
| 653 | |a MAT008000: MAT008000 MATHEMATICS / Discrete Mathematics | ||
| 653 | |a MAT014000: MAT014000 MATHEMATICS / Group Theory | ||
| 653 | |a MAT019000: MAT019000 MATHEMATICS / Matrices | ||
| 653 | |a MAT036000: MAT036000 MATHEMATICS / Combinatorics | ||
| 653 | |a PBD: Discrete mathematics | ||
| 653 | |a PBF: Algebra | ||
| 653 | |a PBV: Combinatorics & graph theory | ||
| 653 | |a Algebraic | ||
| 653 | |a Graph Theory | ||
| 653 | |a Matrices | ||
| 653 | |a Monoids | ||
| 653 | |a Morphisms | ||
| 653 | |a MAT002000 | ||
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Record in the Search Index
| _version_ | 1804180672670072832 |
|---|---|
| adam_text | CONTENTS
PREFACE
*
V
PREFACE
FOR
THE
SECOND
EDITION
*
XI
1
DIRECTED
AND
UNDIRECTED GRAPHS
*
1
1.1
FORMAL
DESCRIPTION
OF
GRAPHS
*
1
1.2
CONNECTEDNESS
AND
EQUIVALENCE
RELATIONS
*
4
1.3
SOME
SPECIAL
GRAPHS
*
5
1.4
HOMOMORPHISMS
*
8
1.5
HALF-,
LOCALLY,
QUASI-STRONG,
AND
METRIC
HOMOMORPHISMS
*
12
1.6
THE
FACTOR
GRAPH,
CONGRUENCES,
AND
THE
HOMOMORPHISM
THEOREM
*
15
FACTOR
GRAPHS
*
15
THE
HOMOMORPHISM
THEOREM
*
17
1.7
THE
ENDOMORPHISM
TYPE
OF
A
GRAPH
*
19
1.8
ON
THE
GENUS
OF
A
GRAPH
*
24
1.9
COMMENTS:
HOMOMORPHISMS
PRODUCE
MODELS
*
27
2
GRAPHS
AND
MATRICES
*
29
2.1
ADJACENCY
MATRIX
*
29
ISOMORPHIC
GRAPHS
AND
THE
ADJACENCY
MATRIX
*
30
COMPONENTS
AND
THE
ADJACENCY
MATRIX
*
31
ADJACENCY
LIST
*
33
2.2
INCIDENCE
MATRIX
*
33
2.3
DISTANCES
IN
GRAPHS
*
34
THE
ADJACENCY
MATRIX
AND
PATHS
*
35
THE
ADJACENCY
MATRIX,
THE
DISTANCE
MATRIX,
AND
CIRCUITS
*
35
2.4
ENDOMORPHISMS
AND
COMMUTING
GRAPHS
*
36
2.5
THE
CHARACTERISTIC
POLYNOMIAL
AND
EIGENVALUES
*
37
2.6
CIRCULANT
GRAPHS
*
41
2.7
EIGENVALUES
AND
THE
COMBINATORIAL
STRUCTURE
*
44
COSPECTRAL
GRAPHS
*
44
EIGENVALUES,
DIAMETER,
AND
REGULARITY
*
45
AUTOMORPHISMS
AND
EIGENVALUES
*
46
2.8
COMMENTS
*
47
3
CATEGORIES
AND
FUNCTORS
*
49
3.1
CATEGORIES
*
49
CATEGORIES
WITH
SETS
AND
MAPPINGS,
I
*
50
CONSTRUCTS,
AND
SMALL
AND
LARGE
CATEGORIES
*
50
XIV
*
*
CONTENTS
SPECIAL
OBJECTS
AND
MORPHISMS
*
51
CATEGORIES
WITH
SETS
AND
MAPPINGS,
II
*
51
CATEGORIES
WITH
GRAPHS
*
52
OTHER
CATEGORIES
*
53
3.2
PRODUCTS
&
CO.
-----
54
COPRODUCTS
*
54
PRODUCTS
*
56
TENSOR
PRODUCTS
*
58
CATEGORIES
WITH
SETS
AND
MAPPINGS,
III
*
58
3.3
FUNCTORS
-----
59
COVARIANT
AND
CONTRAVARIANT
FUNCTORS
*
59
COMPOSITION
OF
FUNCTORS
*
59
SPECIAL
FUNCTORS
*
EXAMPLES
*
60
MOR
FUNCTORS
*
60
PROPERTIES
OF
FUNCTORS
*
61
3.4
COMMENTS
*
63
4
BINARY
GRAPH
OPERATIONS
*
65
4.1
UNIONS
*
65
THE
UNION
*
65
THE
JOIN
-----
67
THE
EDGE
SUM
*
67
4.2
PRODUCTS
-----
71
THE
CROSS
PRODUCT
*
71
THE
COAMALGAMATED
PRODUCT
*
73
THE
DISJUNCTION
OF
GRAPHS
*
75
4.3
TENSOR
PRODUCTS
AND
THE
PRODUCT
IN
EGRA
*
75
THE
BOX
PRODUCT
*
75
THE
BOXCROSS
PRODUCT
*
78
THE
COMPLETE
PRODUCT
*
79
SYNOPSIS
OF
THE
RESULTS
*
79
PRODUCT
CONSTRUCTIONS
AS
FUNCTORS
IN
ONE
VARIABLE
*
80
4.4
LEXICOGRAPHIC
PRODUCTS
AND
THE
CORONA
*
80
LEXICOGRAPHIC
PRODUCTS
*
80
THE
CORONA
*
82
4.5
ALGEBRAIC
PROPERTIES
*
83
4.6
MOR
CONSTRUCTIONS
-----
84
DIAMOND
PRODUCTS
*
84
LEFT
INVERSES
FOR
TENSOR
FUNCTORS
*
86
POWER
PRODUCTS
*
87
LEFT
INVERSES
TO
PRODUCT
FUNCTORS
*
88
4.7
COMMENTS
-----
89
CONTENTS
*
XV
5
LINE
GRAPH
AND
OTHER
UNARY
GRAPH
OPERATIONS
*
91
5.1
COMPLEMENTS,
OPPOSITE
GRAPHS,
AND
GEOMETRIC
DUALS
*
91
5.2
THE
LINE
GRAPH
*
92
DETERMINABILITY
OF
G
BY
LG
*
95
5.3
SPECTRA
OF
LINE
GRAPHS
*
97
WHICH
GRAPHS
ARE
LINE
GRAPHS?
*
100
5.4
THE
TOTAL
GRAPH
*
102
5.5
THE
TREE
GRAPH
-----
103
5.6
COMMENTS
*
103
6
GRAPHS
AND
VECTOR
SPACES
*
105
6.1
VERTEX
SPACE
AND
EDGE
SPACE
*
105
THE
BOUNDARY
AND
CO.
*
106
MATRIX
REPRESENTATION
*
107
6.2
CYCLE
SPACES,
BASES
&
CO.
*
108
THE
CYCLE
SPACE
*
108
THE
COCYCLE
SPACE
*
110
ORTHOGONALITY
*
111
THE
BOUNDARY
OPERATOR
&
CO.
*
113
6.3
APPLICATION:
MACLANE S
PLANARITY
CRITERION
*
114
6.4
HOMOLOGY
OF
GRAPHS
*
116
EXACT
SEQUENCES
OF
VECTOR
SPACES
*
117
CHAIN
COMPLEXES
AND
HOMOLOGY
GROUPS
OF
GRAPHS
*
117
6.5
APPLICATION:
NUMBER
OF
SPANNING
TREES
*
119
6.6
APPLICATION:
ELECTRICAL
NETWORKS
*
123
6.7
APPLICATION:
SQUARED
RECTANGLES
*
128
6.8
APPLICATION:
TRANSPORT
AND
SHORTEST
PATHS
*
132
6.9
COMMENTS
*
135
7
GRAPHS,
GROUPS,
AND
MONOIDS
*
137
7.1
GROUPS
OF
A
GRAPH
*
137
EDGE
GROUP
*
138
7.2
ASYMMETRIC
GRAPHS
AND
RIGID
GRAPHS
*
138
7.3
CAYLEY
GRAPHS
*
145
7.4
FRUCHT-TYPE
RESULTS
*
147
FRUCHT
*
S
THEOREM
AND
ITS
GENERALIZATION
FOR
MONOIDS
*
148
7.5
GRAPH-THEORETIC
REQUIREMENTS
*
149
SMALLEST
GRAPHS
FOR
GIVEN
GROUPS
*
149
ADDITIONAL
PROPERTIES
OF
GROUP-REALIZING
GRAPHS
*
150
7.6
TRANSFORMATION
MONOIDS
AND
PERMUTATION
GROUPS
*
154
7.7
ACTIONS
ON
GRAPHS
*
156
TRANSITIVE
ACTIONS
ON
GRAPHS
*
157
XVI
*
CONTENTS
REGULAR
ACTIONS
*
158
FIXED
POINT-FREE
ACTIONS
ON
GRAPHS
*
160
7.8
COMMENTS
------
161
8
THE
CHARACTERISTIC
POLYNOMIAL
OF
GRAPHS
*
163
8.1
EIGENVECTORS
OF
SYMMETRIC
MATRICES
*
163
EIGENVALUES
AND
CONNECTEDNESS
*
164
REGULAR
GRAPHS
AND
EIGENVALUES
*
165
8.2
INTERPRETATION
OF
THE
COEFFICIENTS
OF
CHAPO(G)
*
166
INTERPRETATION
OF
THE
COEFFICIENTS
FOR
UNDIRECTED
GRAPHS
*
167
8.3
CHARACTERISTIC
POLYNOMIALS
OF
TREES
*
169
8.4
THE
SPECTRAL
RADIUS
OF
UNDIRECTED
GRAPHS
*
170
SUBGRAPHS
*
170
UPPER
BOUNDS
*
171
LOWER
BOUNDS
*
172
8.5
SPECTRAL
DETERMINABILITY
*
173
SPECTRAL
UNIQUENESS
OFK*
AND
K
PQ
*
173
8.6
EIGENVALUES
AND
GROUP
ACTIONS
*
175
GROUPS,
ORBITS,
AND
EIGENVALUES
*
176
8.7
TRANSITIVE
GRAPHS
AND
EIGENVALUES
*
177
DEROGATORY
GRAPHS
*
178
GRAPHS
WITH
ABELIAN
GROUPS
*
179
8.8
COMMENTS
*
180
9
GRAPHS
AND
SEMIGROUPS
*
183
9.1
SEMIGROUPS
*
183
9.2
END-REGULAR
BIPARTITE
GRAPHS
*
187
REGULAR
ENDOMORPHISMS
AND
RETRACTS
*
187
END-REGULAR
AND
END-ORTHODOX
CONNECTED
BIPARTITE
GRAPHS
*
188
9.3
LOCALLY
STRONG
ENDOMORPHISMS
OF
PATHS
*
189
UNDIRECTED
PATHS
*
190
DIRECTED
PATHS
*
192
ALGEBRAIC
PROPERTIES
OF
LEND
*
195
9.4
WREATH
PRODUCT
OF
MONOIDS
OVER
AN
ACT
*
197
9.5
STRUCTURE
OF
THE
STRONG
MONOID
*
200
THE
CANONICAL
STRONG
DECOMPOSITION
OF
6
*
200
DECOMPOSITION
OF
SEND
-----
202
A
GENERALIZED
WREATH
PRODUCT
WITH
A
SMALL
CATEGORY
*
204
CARDINALITY
OF
SEND(G)
*
205
REGULARITY
AND
MORE
FOR
I
A
*
206
REGULARITY
AND
MORE
FOR
SEND(G)
*
206
9.6
COMMENTS
-----
208
CONTENTS
XVII
10
10.1
10.2
10.3
10.4
10.5
10.6
11
11.1
11.2
11.3
11.4
12
12.1
12.2
12.3
12.4
12.5
13
13.1
13.2
COMPOSITIONS,
UNRETRACTIVITIES,
AND
MONOIDS
*
209
LEXICOGRAPHIC
PRODUCTS
*
209
UNRETRACTIVITIES
AND
LEXICOGRAPHIC
PRODUCTS
*
211
MONOIDS
AND
LEXICOGRAPHIC
PRODUCTS
*
214
THE
UNION
AND
THE
JOIN
*
217
THE
SUM
OF
MONOIDS
*
217
THE
SUM
OF
ENDOMORPHISM
MONOIDS
*
218
UNRETRACTIVITIES
*
219
THE
BOX
PRODUCT
AND
THE
CROSS
PRODUCT
*
220
UNRETRACTIVITIES
*
221
THE
PRODUCT
OF
ENDOMORPHISM
MONOIDS
*
222
COMMENTS
-----
223
CAYLEY
GRAPHS
OF
SEMIGROUPS
*
225
THE
CAY
FUNCTOR
*
225
REFLECTION
AND
PRESERVATION
OF
MORPHISMS
*
227
DOES
CAY
PRODUCE
STRONG
HOMOMORPHISMS?
*
228
PRODUCTS
AND
EQUALIZERS
*
229
CATEGORICAL
PRODUCTS
*
229
EQUALIZERS
*
231
OTHER
PRODUCT
CONSTRUCTIONS
*
232
CHARACTERIZATIONS
OF
CAYLEY
GRAPHS
*
234
CAYLEY
GRAPHS
OF
RIGHT
AND
LEFT
GROUPS
*
235
CAYLEY
GRAPHS
OF
STRONG
SEMILATTICES
OF
SEMIGROUPS
*
237
GENERATING
CONNECTION
SETS
*
238
EXAMPLES
OF
STRONG
SEMILATTICES
OF
(RIGHT
OR
LEFT)
GROUPS
*
241
COMMENTS
*
245
VERTEX
TRANSITIVE
CAYLEY
GRAPHS
*
247
VERTEX
TRANSITIVITY
*
247
APPLICATION
TO
STRONG
SEMILATTICES
OF
RIGHT
GROUPS
*
248
COLAUT(S,
OVERTEX
TRANSITIVITY
*
250
AUT(S,
C)-VERTEX
TRANSITIVITY
*
251
APPLICATION
TO
STRONG
SEMILATTICES
OF
LEFT
GROUPS
*
253
APPLICATION
TO
CLIFFORD
SEMIGROUPS
*
256
END (S,
C)-VERTEX
TRANSITIVE
CAYLEY
GRAPHS
*
257
COMMENTS
*
260
EMBEDDINGS
OF
CAYLEY
GRAPHS-GENUS
OF
SEMIGROUPS
*
261
THE
GENUS
OF
A
GROUP
*
261
VARIOUS
RESULTS
AND
QUESTIONS
ABOUT
GENERA
*
268
ON
THE
GENUS
OF
RIGHT
GROUPS
*
269
XVIII
*
CONTENTS
PLANAR
RIGHT
GROUPS
*
270
RIGHT
GROUPS
GENERATED
BY
PRODUCTS
ON
THE
TORUS
AND
THE
PLANE
*
279
13.3
ON
PLANAR
CLIFFORD
SEMIGROUPS
*
284
PLANAR
SEMI
LATTICES
*
285
PLANAR
CLIFFORD
SEMIGROUPS
WITH
TWO
GROUPS
*
287
13.4
COMMENTS
-----
300
LIST
OF
CITED
PAPERS,
THESES
ETC.
*
303
LIST
OF
BOOKS
*
307
INDEX
*
319
INDEX
OF
SYMBOLS
*
327
|
| any_adam_object | 1 |
| author | Knauer, Ulrich 1942- Knauer, Kolja 1980- |
| author_GND | (DE-588)14404787X (DE-588)1197265635 |
| author_facet | Knauer, Ulrich 1942- Knauer, Kolja 1980- |
| author_role | aut aut |
| author_sort | Knauer, Ulrich 1942- |
| author_variant | u k uk k k kk |
| building | Verbundindex |
| bvnumber | BV046248320 |
| classification_rvk | SK 890 |
| ctrlnum | (OCoLC)1083224665 (DE-599)DNB1175757470 |
| discipline | Mathematik |
| edition | 2nd edition |
| format | Book |
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| genre | (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV046248320 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T08:39:29Z |
| institution | BVB |
| institution_GND | (DE-588)10095502-2 |
| isbn | 9783110616125 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-031626586 |
| oclc_num | 1083224665 |
| open_access_boolean | |
| owner | DE-29T DE-11 DE-20 DE-188 |
| owner_facet | DE-29T DE-11 DE-20 DE-188 |
| physical | XVIII, 329 Seiten Illustrationen, Diagramme |
| publishDate | 2019 |
| publishDateSearch | 2019 |
| publishDateSort | 2019 |
| publisher | De Gruyter |
| record_format | marc |
| series | De Gruyter studies in mathematics |
| series2 | De Gruyter studies in mathematics |
| spelling | Knauer, Ulrich 1942- Verfasser (DE-588)14404787X aut Algebraic graph theory morphisms, monoids and matrices Ulrich Knauer and Kolja Knauer 2nd edition Berlin/Boston De Gruyter [2019] © 2019 XVIII, 329 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier De Gruyter studies in mathematics Volume 41 Algebra (DE-588)4001156-2 gnd rswk-swf Graphentheorie (DE-588)4113782-6 gnd rswk-swf Fachpublikum/ Wissenschaft MAT002000 MAT008000: MAT008000 MATHEMATICS / Discrete Mathematics MAT014000: MAT014000 MATHEMATICS / Group Theory MAT019000: MAT019000 MATHEMATICS / Matrices MAT036000: MAT036000 MATHEMATICS / Combinatorics PBD: Discrete mathematics PBF: Algebra PBV: Combinatorics & graph theory Algebraic Graph Theory Matrices Monoids Morphisms (DE-588)4123623-3 Lehrbuch gnd-content Graphentheorie (DE-588)4113782-6 s Algebra (DE-588)4001156-2 s DE-604 Knauer, Kolja 1980- Verfasser (DE-588)1197265635 aut Walter de Gruyter GmbH & Co. KG (DE-588)10095502-2 pbl Erscheint auch als Online-Ausgabe, PDF 978-3-11-061736-8 Erscheint auch als Online-Ausgabe, EPUB 978-3-11-061628-6 De Gruyter studies in mathematics Volume 41 (DE-604)BV000005407 41 B:DE-101 application/pdf https://d-nb.info/1175757470/04 Inhaltsverzeichnis DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031626586&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Knauer, Ulrich 1942- Knauer, Kolja 1980- Algebraic graph theory morphisms, monoids and matrices De Gruyter studies in mathematics Algebra (DE-588)4001156-2 gnd Graphentheorie (DE-588)4113782-6 gnd |
| subject_GND | (DE-588)4001156-2 (DE-588)4113782-6 (DE-588)4123623-3 |
| title | Algebraic graph theory morphisms, monoids and matrices |
| title_auth | Algebraic graph theory morphisms, monoids and matrices |
| title_exact_search | Algebraic graph theory morphisms, monoids and matrices |
| title_full | Algebraic graph theory morphisms, monoids and matrices Ulrich Knauer and Kolja Knauer |
| title_fullStr | Algebraic graph theory morphisms, monoids and matrices Ulrich Knauer and Kolja Knauer |
| title_full_unstemmed | Algebraic graph theory morphisms, monoids and matrices Ulrich Knauer and Kolja Knauer |
| title_short | Algebraic graph theory |
| title_sort | algebraic graph theory morphisms monoids and matrices |
| title_sub | morphisms, monoids and matrices |
| topic | Algebra (DE-588)4001156-2 gnd Graphentheorie (DE-588)4113782-6 gnd |
| topic_facet | Algebra Graphentheorie Lehrbuch |
| url | https://d-nb.info/1175757470/04 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031626586&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000005407 |
| work_keys_str_mv | AT knauerulrich algebraicgraphtheorymorphismsmonoidsandmatrices AT knauerkolja algebraicgraphtheorymorphismsmonoidsandmatrices AT walterdegruytergmbhcokg algebraicgraphtheorymorphismsmonoidsandmatrices |
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