Graph dynamics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Harlow
Longman
1995
|
| Edition: | 1. publication |
| Series: | Pitman Research Notes in Mathematics Series
338 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Zugl.: Diss. |
| Physical Description: | 233 Seiten graph. Darst. |
| ISBN: | 0582286964 |
Staff View
MARC
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| 100 | 1 | |a Prisner, Erich |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Graph dynamics |c Erich Prisner, Universität Hamburg, Germany and Clemson University, USA |
| 250 | |a 1. publication | ||
| 264 | 1 | |a Harlow |b Longman |c 1995 | |
| 300 | |a 233 Seiten |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Pitman Research Notes in Mathematics Series |v 338 | |
| 500 | |a Zugl.: Diss. | ||
| 650 | 7 | |a Grafentheorie |2 gtt | |
| 650 | 7 | |a Graphes, Théorie des |2 ram | |
| 650 | 4 | |a Graph theory | |
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Record in the Search Index
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| adam_text | Contents
0 INTRODUCTION 1
0.1 A sketch of the history 1
0.2 Scope of this monograph 2
0.3 Graph theoretic terminology 4
1 THEORY FOR GENERAL OPERATORS 9
1 Discrete dynamical systems 11
2 Fixed graphs 18
3 Increasing parameters, divergence and depth 23
3.1 Case study: The line graph 24
3.2 Parameter examples: The touching numbers tn(G) 26
4 Non increasing parameters and convergence 30
4.1 An example: w and $k,k+i 31
4.2 Diameter — another useful parameter 32
5 Invariants 36
5.1 Betti numbers 36
5.2 Invariance and convergence towards 38
5.3 Non increasing and non decreasing parameters 41
6 Connected components 43
6.1 The quasidigraph 43
6.2 Strong components and inverse rays 46
6.3 Components of periodic graphs 48
6.4 Periodic units and quasifmite graphs 49
6.5 Convergence and out locally finiteness 52
6.6 The case of out degrees 0 or 1 53
6.7 A non graphical example 54
7 Subgraph defined operators 57
7.1 The general case 57
7.2 Intersection graph operators 58
7.3 Intersection digraph operators 59
7.4 Automorphisms 60
7.5 Some axioms 61
7.6 Distant relatives 63
8 Constructing infinite periodic graphs 65
8.1 The basic conditions 67
8.2 A modification 69
8.3 The digraph case 70
9 Admissible graph posets 72
9.1 Characterizations of convergent graphs 74
9.2 Mortality 77
9.3 Depth of divergent finite graphs 78
10 Roots 80
10.1 Dualization Characterizations 80
10.2 Generalized dualization characterizations 82
10.3 Forbidden (induced) subgraphs . .• 83
10.4 Unique roots or quasiroots 84
10.5 Finite number of roots or quasiroots 85
10.6 Distinguished roots 85
11 Decision problems 88
11.1 Deciding convergence 89
11.2 Deciding mortality or convergence towards 90
11.3 Recognition of $ graphs 91
11.4 Bounds for the depth 93
12 Powerlike operators 97
12.1 The quasidigraph 97
12.1.1 When is $(G) connected? 98
12.1.2 Periodic graphs containing a given component 100
12.2 Coloured graphs 100
13 Miscellaneous tools 104
13.1 Shrinking or expanding operators 104
13.1.1 Case study: Clique line graph 104
13.1.2 Elimination schemes 107
13.2 Composed operators 108
13.3 Majorizing operators Ill
13.4 New systems from old ones 112
13.4.1 Foldings between systems 112
13.4.2 Powers of systems 115
II CONCRETE OPERATORS 117
14 Intersection graph operators 119
14.1 Line graph L(G) 119
14.2 Middle graph Mid(G) 120
14.3 Clique graph C(G) 122
14.3.1 The C semibasin of clique Helly graphs 123
14.3.2 The general case 124
14.4 Simplex graph Simp(G) 127
14.5 fc edge graph X7k(G) 128
14.6 Block graph B(G) 130
14.7 /f intersection graph 131
15 Other subgraph defined operators 132
15.1 fc Gallai graph galk(G) 132
15.2 The k m m graph $k,m 136
15.3 fc line graph Lk ...... 138
15.4 fc path graph Vathk(G) 140
15.5 A; overlap clique graph Ck(G) 142
15.6 Cycle graph Cy(G) 143
15.7 fc vertex graph Vertk(G) 145
15.8 fc rotation graph Uotk(G) 146
15.9 fc super line graph Slk(G) 146
15.10 /Mine graphs LH(G) 148
15.11 More operators 148
15.11.1 Wing graph 148
15.11.2 Edge graph 149
15.11.3 1 factor graph 149
15.11.4 Tree graphs t(G),t2(G) 149
15.11.5 fc total graphs Tk(G) 150
15.11.6 Second iterated line graph 150
15.11.7 Zelinka s operator 150
15.11.8 Block point tree, semitotal block graph, total block graph 150
15.11.9 Plick graph and glick graph 150
16 Powerlike operators 152
16.1 Complement G 152
16.2 Powers Powk{G) 152
16.3 fc step graphs Stepk(G) 154
16.3.1 The odd k case 155
16.3.2 The even k case 156
16.4 A: distance graphs Tk(G) 157
16.5 Antipodal graph A(G) 159
16.6 The closed neighbourhood containment graph Afcon(G) 162
16.7 The pseudoinverse graph Vi(G) 166
16.8 More operators 168
16.8.1 fc path step graphs S k(G) 168
16.8.2 Eccentric graph £cc(G) 169
16.8.3 Hamiltonian path graph Ham(G) 169
17 Shrinking or expanding operators 171
17.1 Centre Z{G) 171
17.1.1 Chordal connected graphs 172
17.2 Median Med(G) 174
17.3 Induced path centroid Centi 174
17.4 Subdivisions Subdk 175
17.5 Total graph T(G) 176
17.6 More operators 177
17.6.1 The fc centrum 177
17.6.2 Anticentre or periphery ACent(G) 178
17.6.3 Antimedian AMed(G) 178
17.6.4 Shortest path centroid Cents 178
17.6.5 Pruned graph P(G) 179
17.6.6 Semitotal point graph SemiT(G) 179
17.6.7 Bosak s operator 179
17.6.8 Steiner fc centres 180
18 Composed operators 181
18.1 Line graph and complement 181
18.2 Powers and complement 184
18.3 Clique graph and line graph 185
18.4 Line graph and square 188
18.5 fc offspring 189
18.6 ^ partial line graph 190
18.7 Cutpoint graph Art(G) 191
18.8 Block cutpoint tree bc(G) 191
18.9 More compositions 192
18.9.1 Line graph and subdivision 192
18.9.2 n subgraph (rotation) distance graph 193
18.9.3 Total graph and complement 193
18.9.4 Block graph and middle graph 193
18.9.5 Clique graph and middle graph 193
18.9.6 Clique graph and total graph 193
18.9.7 path step graphs and complement 193
18.9.8 fcth iterated line graph and complement 194
18.9.9 Forcing graph and complement 194
18.9.10 Eccentric graph and complement 194
19 Digraph operators 195
19.1 Line digraph L(D) 195
19.2 Powers Powk{D) of digraphs 200
19.3 Total digraph f(D) 201
19.4 Biclique digraph C(D) 201
19.5 More operators 204
19.5.1 The reversal D~ 204
19.5.2 The complement ~D 204
19.5.3 Line digraph and reversal 204
19.5.4 Subdivision digraphs 205
19.5.5 Middle digraph M(D) 205
19.5.6 In and out centre and periphery 206
19.5.7 Multidimensional line digraphs 206
19.5.8 Two step digraphs 207
. Bibliography 208
. Index 230
|
| any_adam_object | 1 |
| author | Prisner, Erich |
| author_facet | Prisner, Erich |
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| indexdate | 2024-07-09T17:56:37Z |
| institution | BVB |
| isbn | 0582286964 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007107214 |
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| physical | 233 Seiten graph. Darst. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
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| publisher | Longman |
| record_format | marc |
| series | Pitman Research Notes in Mathematics Series |
| series2 | Pitman Research Notes in Mathematics Series |
| spelling | Prisner, Erich Verfasser aut Graph dynamics Erich Prisner, Universität Hamburg, Germany and Clemson University, USA 1. publication Harlow Longman 1995 233 Seiten graph. Darst. txt rdacontent n rdamedia nc rdacarrier Pitman Research Notes in Mathematics Series 338 Zugl.: Diss. Grafentheorie gtt Graphes, Théorie des ram Graph theory Graphentheorie (DE-588)4113782-6 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Graphentheorie (DE-588)4113782-6 s DE-604 Pitman Research Notes in Mathematics Series 338 (DE-604)BV000022845 338 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007107214&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Prisner, Erich Graph dynamics Pitman Research Notes in Mathematics Series Grafentheorie gtt Graphes, Théorie des ram Graph theory Graphentheorie (DE-588)4113782-6 gnd |
| subject_GND | (DE-588)4113782-6 (DE-588)4113937-9 |
| title | Graph dynamics |
| title_auth | Graph dynamics |
| title_exact_search | Graph dynamics |
| title_full | Graph dynamics Erich Prisner, Universität Hamburg, Germany and Clemson University, USA |
| title_fullStr | Graph dynamics Erich Prisner, Universität Hamburg, Germany and Clemson University, USA |
| title_full_unstemmed | Graph dynamics Erich Prisner, Universität Hamburg, Germany and Clemson University, USA |
| title_short | Graph dynamics |
| title_sort | graph dynamics |
| topic | Grafentheorie gtt Graphes, Théorie des ram Graph theory Graphentheorie (DE-588)4113782-6 gnd |
| topic_facet | Grafentheorie Graphes, Théorie des Graph theory Graphentheorie Hochschulschrift |
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