Graphs and applications: an introductory approach
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | Undetermined |
| Published: |
London [u.a.]
Springer
2007
|
| Edition: | 6. print. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 444 S. graph. Darst. 1 CD-ROM (12 cm) |
| ISBN: | 185233259X |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804138798010859520 |
|---|---|
| adam_text | JOAN M. ALDOUS AND ROBIN J. WILSON GRAPHS AND APPLICATIONS AN
INTRODUCTORY APPROACH WITH 644 ILLUSTRATIONS BY STEVE BEST SPRINGER
CONTENTS 1 INTRODUCTION 1 1.1 GRAPHS, DIGRAPHS AND NETWORKS 1 1.2
CLASSIFYING PROBLEMS 20 1.3 SEEKING SOLUTIONS 23 2 GRAPHS 25 2.1 GRAPHS
AND SUBGRAPHS 25 2.2 VERTEX DEGREES 35 2.3 PATHS AND CYCLES 38 2.4
REGULAR AND BIPARTITE GRAPHS 43 2.5 CASE STUDIES 50 FOUR CUBES PROBLEM
51 SOCIAL NETWORKS 53 EXERCISES 2 56 3 EULERIAN AND HAMILTONIAN GRAPHS
61 3.1 EXPLORING AND TRAVELLING 61 3.2 EULERIAN GRAPHS 64 3.3
HAMILTONIAN GRAPHS 71 3.4 CASE STUDIES 75 DOMINOES 75 DIAGRAM-TRACING
PUZZLES 76 KNIGHT S TOUR PROBLEM 78 GRAY CODES 80 EXERCISES 3 82 4
DIGRAPHS 84 4.1 DIGRAPHS AND SUBDIGRAPHS 84 4.2 VERTEX DEGREES 92 4.3
PATHS AND CYCLES 94 4.4 EULERIAN AND HAMILTONIAN DIGRAPHS 97 4.5 CASE
STUDIES 99 ECOLOGY 99 X GRAPHS AND APPLICATIONS: AN INTRODUCTORY
APPROACH SOCIAL NETWORKS 101 ROTATING DRUM PROBLEM 104 RANKING IN
TOURNAMENTS 106 EXERCISES 4 108 5 MATRIX REPRESENTATIONS 112 5.1
ADJACENCY MATRICES 113 5.2 WALKS IN GRAPHS AND DIGRAPHS 117 5.3
INCIDENCE MATRICES 122 5.4 CASE STUDIES 126 INTERVAL GRAPHS 126 MARKOV
CHAINS 129 EXERCISES 5 133 6 TREE STRUCTURES 138 6.1 MATHEMATICAL
PROPERTIES OF TREES 140 6.2 SPANNING TREES 144 6.3 ROOTED TREES 146 6.4
CASE STUDY 152 BRACED RECTANGULAR FRAMEWORKS 152 EXERCISES 6 161 7
COUNTING TREES 163 7.1 COUNTING LABELLED TREES 164 7.2 COUNTING BINARY
TREES 171 7.3 COUNTING CHEMICAL TREES 174 EXERCISES 7 181 8 GREEDY
ALGORITHMS 182 8.1 MINIMUM CONNECTOR PROBLEM 182 8.2 TRAVELLING SALESMAN
PROBLEM 191 EXERCISES 8 198 9 PATH ALGORITHMS 202 9.1 FLEURY S ALGORITHM
202 9.2 SHORTEST PATH ALGORITHM 204 9.3 CASE STUDY 212 CHINESE POSTMAN
PROBLEM 212 EXERCISES 9 214 10 PATHS AND CONNECTIVITY 216 10.1 CONNECTED
GRAPHS AND DIGRAPHS 216 10.2 MENGER S THEOREM FOR GRAPHS 226 10.3 SOME
ANALOGUES OF MENGER S THEOREM 230 10.4 CASE STUDY 236 CONTENTS XI
RELIABLE TELECOMMUNICATION NETWORKS 236 EXERCISES 10 239 11 PLANARITY
242 11.1 PLANAR GRAPHS 243 11.2 EULER S FORMULA 247 11.3 CYCLE METHOD
FOR PLANARITY TESTING 256 11.4 KURATOWSKI S THEOREM 260 11.5 DUALITY 264
11.6 CONVEX POLYHEDRA 268 EXERCISES 11 274 12 VERTEX COLOURINGS AND
DECOMPOSITIONS ... 277 12.1 VERTEX COLOURINGS 277 12.2 ALGORITHM FOR
VERTEX COLOURING 288 12.3 VERTEX DECOMPOSITIONS 292 EXERCISES 12 299 13
EDGE COLOURINGS AND DECOMPOSITIONS .... 303 13.1 EDGE COLOURINGS 303
13.2 ALGORITHM FOR EDGE COLOURING 313 13.3 EDGE DECOMPOSITIONS 317
EXERCISES 13 329 14 CONCLUSION 332 14.1 CLASSIFICATION OF PROBLEMS 332
14.2 EFFICIENCY OF ALGORITHMS 338 14.3 ANOTHER CLASSIFICATION OF
PROBLEMS 339 SUGGESTIONS FOR FURTHER READING 346 APPENDIX: METHODS OF
PROOF 348 COMPUTING NOTES 354 SOLUTIONS TO COMPUTER ACTIVITIES 380
SOLUTIONS TO PROBLEMS IN THE TEXT 384 INDEX 439
|
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| author | Aldous, Joan M. Wilson, Robin J. 1943- |
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| publishDate | 2007 |
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| publisher | Springer |
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| spelling | Aldous, Joan M. Verfasser aut Graphs and applications an introductory approach Joan M. Aldous and Robin J. Wilson 6. print. London [u.a.] Springer 2007 XI, 444 S. graph. Darst. 1 CD-ROM (12 cm) txt rdacontent n rdamedia nc rdacarrier Graph (DE-588)4021842-9 gnd rswk-swf CD-ROM (DE-588)4139307-7 gnd rswk-swf Graphentheorie (DE-588)4113782-6 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Graph (DE-588)4021842-9 s CD-ROM (DE-588)4139307-7 s 2\p DE-604 Graphentheorie (DE-588)4113782-6 s 3\p DE-604 Wilson, Robin J. 1943- Verfasser (DE-588)141760176 aut HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017296625&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 | Aldous, Joan M. Wilson, Robin J. 1943- Graphs and applications an introductory approach Graph (DE-588)4021842-9 gnd CD-ROM (DE-588)4139307-7 gnd Graphentheorie (DE-588)4113782-6 gnd |
| subject_GND | (DE-588)4021842-9 (DE-588)4139307-7 (DE-588)4113782-6 (DE-588)4123623-3 |
| title | Graphs and applications an introductory approach |
| title_auth | Graphs and applications an introductory approach |
| title_exact_search | Graphs and applications an introductory approach |
| title_full | Graphs and applications an introductory approach Joan M. Aldous and Robin J. Wilson |
| title_fullStr | Graphs and applications an introductory approach Joan M. Aldous and Robin J. Wilson |
| title_full_unstemmed | Graphs and applications an introductory approach Joan M. Aldous and Robin J. Wilson |
| title_short | Graphs and applications |
| title_sort | graphs and applications an introductory approach |
| title_sub | an introductory approach |
| topic | Graph (DE-588)4021842-9 gnd CD-ROM (DE-588)4139307-7 gnd Graphentheorie (DE-588)4113782-6 gnd |
| topic_facet | Graph CD-ROM Graphentheorie Lehrbuch |
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