Graph theory and its applications:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton, Fla. [u.a.]
Chapman & Hall/CRC
2006
|
| Edition: | Second edition |
| Series: | Discrete Mathematics and its Applications
|
| Subjects: | |
| Online Access: | Table of contents only Publisher description Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references (S. 695-708) and indexes |
| Physical Description: | 779 Seiten Ill., graph. Darst. |
| ISBN: | 158488505X 9781584885054 |
Staff View
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| 250 | |a Second edition | ||
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Record in the Search Index
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| adam_text | DISCRETE MATHEMATICS AND ITS APPLICATIONS SERIES EDITOR KENNETH H. ROSEN
GRAPH THEORY AND ITS APPLICATIONS SECOND EDITION JONATHAN L GROSS
JAYYELLEN CHAPMAN & HALL/CRC TAYLOR & FRANCIS GROUP BOCA RATON LONDON
NEW YORK CONTENTS PREFACE 1. INTRODUCTION TO GRAPH MODELS 1 1.1 GRAPHS
AND DIGRAPHS 2 1.2 COMMON FAMILIES OF GRAPHS 15 1.3 GRAPH MODELING
APPLICATIONS 22 1.4 WALKS AND DISTANCE 28 1.5 PATHS, CYCLES, AND TREES
39 1.6 VERTEX AND EDGE ATTRIBUTES: MORE APPLICATIONS 48 1.7
SUPPLEMENTARY EXERCISES 51 GLOSSARY 53 2. STRUCTURE AND REPRESENTATION
57 2.1 GRAPH ISOMORPHISM 58 2.2 AUTOMORPHISMS AND SYMMETRY 65 2.3
SUBGRAPHS 72 2.4 SOME GRAPH OPERATIONS 80 2.5 TESTS FOR NON-ISOMORPHISM
89 2.6 MATRIX REPRESENTATIONS 95 2.7 MORE GRAPH OPERATIONS 101 2.8
SUPPLEMENTARY EXERCISES 107 GLOSSARY 110 3. TREES 115 3.1
CHARACTERIZATIONS AND PROPERTIES OF TREES 116 3.2 ROOTED TREES, ORDERED
TREES, AND BINARY TREES 124 3.3 BINARY-TREE TRAVERSALS 132 3.4
BINARY-SEARCH TREES 137 3.5 HUFFMAN TREES AND OPTIMAL PREFIX CODES 141
3.6 PRIORITY TREES 146 3.7 COUNTING LABELED TREES: PRIIFER ENCODING 151
3.8 COUNTING BINARY TREES: CATALAN RECURSION 156 3.9 SUPPLEMENTARY
EXERCISES 158 GLOSSARY 160 4. SPANNING TREES 163 4.1 TREE GROWING 164
4.2 DEPTH-FIRST AND BREADTH-FIRST SEARCH 171 4.3 MINIMUM SPANNING TREES
AND SHORTEST PATHS 176 4.4 APPLICATIONS OF DEPTH-FIRST SEARCH 182 4.5
CYCLES, EDGE-CUTS, AND SPANNING TREES 190 4.6 GRAPHS AND VECTOR SPACES
197 4.7 MATROIDS AND THE GREEDY ALGORITHM 207 4.8 SUPPLEMENTARY
EXERCISES 212 GLOSSARY 213 5. CONNECTIVITY 217 5.1 VERTEX- AND
EDGE-CONNECTIVITY 218 5.2 CONSTRUCTING RELIABLE NETWORKS 223 5.3 MAX-MIN
DUALITY AND MENGER S THEOREMS 231 5.4 BLOCK DECOMPOSITIONS 241 5.5
SUPPLEMENTARY EXERCISES 244 GLOSSARY 245 6. OPTIMAL GRAPH TRAVERSALS 247
6.1 EULERIAN TRAILS AND TOURS 248 6.2 DEBRUIJN SEQUENCES AND POSTMAN
PROBLEMS 252 6.3 HAMILTONIAN PATHS AND CYCLES 267 6.4 GRAY CODES AND
TRAVELING SALESMAN PROBLEMS 273 6.5 SUPPLEMENTARY EXERCISES 282 GLOSSARY
283 7. PLANARITY AND KURATOWSKI S THEOREM 285 7.1 PLANAR DRAWINGS AND
SOME BASIC SURFACES 286 7.2 SUBDIVISION AND HOMEOMORPHISM 292 7.3
EXTENDING PLANAR DRAWINGS 297 7.4 KURATOWSKI S THEOREM 304 7.5 ALGEBRAIC
TESTS FOR PLANARITY 311 7.6 PLANARITY ALGORITHM 324 7.7 CROSSING NUMBERS
AND THICKNESS 327 7.8 SUPPLEMENTARY EXERCISES 331 GLOSSARY 334 8.
DRAWING GRAPHS AND MAPS 337 8.1 THE TOPOLOGY OF LOW DIMENSIONS 338 8.2
HIGHER-ORDER SURFACES 341 8.3 MATHEMATICAL MODEL FOR DRAWING GRAPHS 346
8.4 REGULAR MAPS ON A SPHERE 349 8.5 IMBEDDINGS ON HIGHER-ORDER SURFACES
354 8.6 GEOMETRIC DRAWINGS OF GRAPHS 361 8.7 SUPPLEMENTARY EXERCISES 365
GLOSSARY 366 9. GRAPH COLORINGS 371 J.I VERTEX-COLORINGS 372 9.2
MAP-COLORINGS 386 9.3 EDGE-COLORINGS 393 9.4 FACTORIZATION 407 9.5
SUPPLEMENTARY EXERCISES 411 GLOSSARY 413 10. MEASUREMENT AND MAPPINGS
417 10.1 DISTANCE IN GRAPHS 418 10.2 DOMINATION IN GRAPHS 424 10.3
BANDWIDTH 430 10.4 INTERSECTION GRAPHS 435 10.5 LINEAR GRAPH MAPPINGS
444 10.6 MODELING NETWORK EMULATION 453 10.7 SUPPLEMENTARY EXERCISES 462
GLOSSARY 463 11. ANALYTIC GRAPH THEORY 469 11.1 RAMSEY GRAPH THEORY 470
11.2 EXTREMAL GRAPH THEORY 475 11.3 RANDOM GRAPHS 480 11.4 SUPPLEMENTARY
EXERCISES 489 GLOSSARY 490 12. SPECIAL DIGRAPH MODELS 493 12.1 DIRECTED
PATHS AND MUTUAL REACHABILITY 494 12.2 DIGRAPHS AS MODELS FOR RELATIONS
505 12.3 TOURNAMENTS 511 12.4 PROJECT SCHEDULING AND CRITICAL PATHS 516
12.5 FINDING THE STRONG COMPONENTS OF A DIGRAPH 523 12.6 SUPPLEMENTARY
EXERCISES 528 GLOSSARY 529 13. NETWORK FLOWS AND APPLICATIONS 533 13.1
FLOWS AND CUTS IN NETWORKS 534 13.2 SOLVING THE MAXIMUM-FLOW PROBLEM 542
13.3 FLOWS AND CONNECTIVITY 551 13.4 MATCHINGS, TRANSVERSALS, AND VERTEX
COVERS 560 13.5 SUPPLEMENTARY EXERCISES 573 GLOSSARY 574 14. GRAPHICAL
ENUMERATION 577 14.1 AUTOMORPHISMS OF SIMPLE GRAPHS 578 14.2 GRAPH
COLORINGS AND SYMMETRY 583 14.3 BURNSIDE S LEMMA 589 14.4 CYCLE-INDEX
POLYNOMIAL OF A PERMUTATION GROUP 595 14.5 MORE COUNTING, INCLUDING
SIMPLE GRAPHS 600 14.6 POLYA-BURNSIDE ENUMERATION 606 14.7 SUPPLEMENTARY
EXERCISES 609 GLOSSARY 610 15. ALGEBRAIC SPECIFICATION OF GRAPHS 613
15.1 CYCLIC VOLTAGES 614 15.2 CAYLEY GRAPHS AND REGULAR VOLTAGES 623
15.3 PERMUTATION VOLTAGES 632 15.4 SYMMETRIC GRAPHS AND PARALLEL
ARCHITECTURES 637 15.5 INTERCONNECTION-NETWORK PERFORMANCE 644 15.6
SUPPLEMENTARY EXERCISES 646 GLOSSARY 649 16. NONPLANAR LAYOUTS 651 16.1
REPRESENTING IMBEDDINGS BY ROTATIONS 652 16.2 GENUS DISTRIBUTION OF A
GRAPH 659 16.3 VOLTAGE-GRAPH SPECIFICATION OF GRAPH LAYOUTS 664 16.4
NON-KVL IMBEDDED VOLTAGE GRAPHS 670 16.5 HEAWOOD MAP-COLORING PROBLEM
672 16.6 SUPPLEMENTARY EXERCISES 677 GLOSSARY 678 APPENDIX 681 A.I LOGIC
FUNDAMENTALS 681 A.2 RELATIONS AND FUNCTIONS 683 A.3 SOME BASIC
COMBINATORICS 686 A.4 ALGEBRAIC STRUCTURES 687 A.5 ALGORITHMIC
COMPLEXITY 692 A.6 SUPPLEMENTARY READING 694 BIBLIOGRAPHY 695 B.I
GENERAL READING 695 B.2 REFERENCES 697 SOLUTIONS AND HINTS 709 INDEXES
757 1.1 INDEX OF APPLICATIONS 757 1.2 INDEX OF ALGORITHMS 759 1.3 INDEX
OF NOTATIONS 761 1.4 GENERAL INDEX 767
|
| adam_txt |
DISCRETE MATHEMATICS AND ITS APPLICATIONS SERIES EDITOR KENNETH H. ROSEN
GRAPH THEORY AND ITS APPLICATIONS SECOND EDITION JONATHAN L GROSS
JAYYELLEN CHAPMAN & HALL/CRC TAYLOR & FRANCIS GROUP BOCA RATON LONDON
NEW YORK CONTENTS PREFACE 1. INTRODUCTION TO GRAPH MODELS 1 1.1 GRAPHS
AND DIGRAPHS 2 1.2 COMMON FAMILIES OF GRAPHS 15 1.3 GRAPH MODELING
APPLICATIONS 22 1.4 WALKS AND DISTANCE 28 1.5 PATHS, CYCLES, AND TREES
39 1.6 VERTEX AND EDGE ATTRIBUTES: MORE APPLICATIONS 48 1.7
SUPPLEMENTARY EXERCISES 51 GLOSSARY 53 2. STRUCTURE AND REPRESENTATION
57 2.1 GRAPH ISOMORPHISM 58 2.2 AUTOMORPHISMS AND SYMMETRY 65 2.3
SUBGRAPHS 72 2.4 SOME GRAPH OPERATIONS 80 2.5 TESTS FOR NON-ISOMORPHISM
89 2.6 MATRIX REPRESENTATIONS 95 2.7 MORE GRAPH OPERATIONS 101 2.8
SUPPLEMENTARY EXERCISES 107 GLOSSARY 110 3. TREES 115 3.1
CHARACTERIZATIONS AND PROPERTIES OF TREES 116 3.2 ROOTED TREES, ORDERED
TREES, AND BINARY TREES 124 3.3 BINARY-TREE TRAVERSALS 132 3.4
BINARY-SEARCH TREES 137 3.5 HUFFMAN TREES AND OPTIMAL PREFIX CODES 141
3.6 PRIORITY TREES 146 3.7 COUNTING LABELED TREES: PRIIFER ENCODING 151
3.8 COUNTING BINARY TREES: CATALAN RECURSION 156 3.9 SUPPLEMENTARY
EXERCISES 158 GLOSSARY 160 4. SPANNING TREES 163 4.1 TREE GROWING 164
4.2 DEPTH-FIRST AND BREADTH-FIRST SEARCH 171 4.3 MINIMUM SPANNING TREES
AND SHORTEST PATHS 176 4.4 APPLICATIONS OF DEPTH-FIRST SEARCH 182 4.5
CYCLES, EDGE-CUTS, AND SPANNING TREES 190 4.6 GRAPHS AND VECTOR SPACES
197 4.7 MATROIDS AND THE GREEDY ALGORITHM 207 4.8 SUPPLEMENTARY
EXERCISES 212 GLOSSARY 213 5. CONNECTIVITY 217 5.1 VERTEX- AND
EDGE-CONNECTIVITY 218 5.2 CONSTRUCTING RELIABLE NETWORKS 223 5.3 MAX-MIN
DUALITY AND MENGER'S THEOREMS 231 5.4 BLOCK DECOMPOSITIONS 241 5.5
SUPPLEMENTARY EXERCISES 244 GLOSSARY 245 6. OPTIMAL GRAPH TRAVERSALS 247
6.1 EULERIAN TRAILS AND TOURS 248 6.2 DEBRUIJN SEQUENCES AND POSTMAN
PROBLEMS 252 6.3 HAMILTONIAN PATHS AND CYCLES 267 6.4 GRAY CODES AND
TRAVELING SALESMAN PROBLEMS 273 6.5 SUPPLEMENTARY EXERCISES 282 GLOSSARY
283 7. PLANARITY AND KURATOWSKI'S THEOREM 285 7.1 PLANAR DRAWINGS AND
SOME BASIC SURFACES 286 7.2 SUBDIVISION AND HOMEOMORPHISM 292 7.3
EXTENDING PLANAR DRAWINGS 297 7.4 KURATOWSKI'S THEOREM 304 7.5 ALGEBRAIC
TESTS FOR PLANARITY 311 7.6 PLANARITY ALGORITHM 324 7.7 CROSSING NUMBERS
AND THICKNESS 327 7.8 SUPPLEMENTARY EXERCISES 331 GLOSSARY 334 8.
DRAWING GRAPHS AND MAPS 337 8.1 THE TOPOLOGY OF LOW DIMENSIONS 338 8.2
HIGHER-ORDER SURFACES 341 8.3 MATHEMATICAL MODEL FOR DRAWING GRAPHS 346
8.4 REGULAR MAPS ON A SPHERE 349 8.5 IMBEDDINGS ON HIGHER-ORDER SURFACES
354 8.6 GEOMETRIC DRAWINGS OF GRAPHS 361 8.7 SUPPLEMENTARY EXERCISES 365
GLOSSARY 366 9. GRAPH COLORINGS 371 J.I VERTEX-COLORINGS 372 9.2
MAP-COLORINGS 386 9.3 EDGE-COLORINGS 393 9.4 FACTORIZATION 407 9.5
SUPPLEMENTARY EXERCISES 411 GLOSSARY 413 10. MEASUREMENT AND MAPPINGS
417 10.1 DISTANCE IN GRAPHS 418 10.2 DOMINATION IN GRAPHS 424 10.3
BANDWIDTH 430 10.4 INTERSECTION GRAPHS 435 10.5 LINEAR GRAPH MAPPINGS
444 10.6 MODELING NETWORK EMULATION 453 10.7 SUPPLEMENTARY EXERCISES 462
GLOSSARY 463 11. ANALYTIC GRAPH THEORY 469 11.1 RAMSEY GRAPH THEORY 470
11.2 EXTREMAL GRAPH THEORY 475 11.3 RANDOM GRAPHS 480 11.4 SUPPLEMENTARY
EXERCISES 489 GLOSSARY 490 12. SPECIAL DIGRAPH MODELS 493 12.1 DIRECTED
PATHS AND MUTUAL REACHABILITY 494 12.2 DIGRAPHS AS MODELS FOR RELATIONS
505 12.3 TOURNAMENTS 511 12.4 PROJECT SCHEDULING AND CRITICAL PATHS 516
12.5 FINDING THE STRONG COMPONENTS OF A DIGRAPH 523 12.6 SUPPLEMENTARY
EXERCISES 528 GLOSSARY 529 13. NETWORK FLOWS AND APPLICATIONS 533 13.1
FLOWS AND CUTS IN NETWORKS 534 13.2 SOLVING THE MAXIMUM-FLOW PROBLEM 542
13.3 FLOWS AND CONNECTIVITY 551 13.4 MATCHINGS, TRANSVERSALS, AND VERTEX
COVERS 560 13.5 SUPPLEMENTARY EXERCISES 573 GLOSSARY 574 14. GRAPHICAL
ENUMERATION 577 14.1 AUTOMORPHISMS OF SIMPLE GRAPHS 578 14.2 GRAPH
COLORINGS AND SYMMETRY 583 14.3 BURNSIDE'S LEMMA 589 14.4 CYCLE-INDEX
POLYNOMIAL OF A PERMUTATION GROUP 595 14.5 MORE COUNTING, INCLUDING
SIMPLE GRAPHS 600 14.6 POLYA-BURNSIDE ENUMERATION 606 14.7 SUPPLEMENTARY
EXERCISES 609 GLOSSARY 610 15. ALGEBRAIC SPECIFICATION OF GRAPHS 613
15.1 CYCLIC VOLTAGES 614 15.2 CAYLEY GRAPHS AND REGULAR VOLTAGES 623
15.3 PERMUTATION VOLTAGES 632 15.4 SYMMETRIC GRAPHS AND PARALLEL
ARCHITECTURES 637 15.5 INTERCONNECTION-NETWORK PERFORMANCE 644 15.6
SUPPLEMENTARY EXERCISES 646 GLOSSARY 649 16. NONPLANAR LAYOUTS 651 16.1
REPRESENTING IMBEDDINGS BY ROTATIONS 652 16.2 GENUS DISTRIBUTION OF A
GRAPH 659 16.3 VOLTAGE-GRAPH SPECIFICATION OF GRAPH LAYOUTS 664 16.4
NON-KVL IMBEDDED VOLTAGE GRAPHS 670 16.5 HEAWOOD MAP-COLORING PROBLEM
672 16.6 SUPPLEMENTARY EXERCISES 677 GLOSSARY 678 APPENDIX 681 A.I LOGIC
FUNDAMENTALS 681 A.2 RELATIONS AND FUNCTIONS 683 A.3 SOME BASIC
COMBINATORICS 686 A.4 ALGEBRAIC STRUCTURES 687 A.5 ALGORITHMIC
COMPLEXITY 692 A.6 SUPPLEMENTARY READING 694 BIBLIOGRAPHY 695 B.I
GENERAL READING 695 B.2 REFERENCES 697 SOLUTIONS AND HINTS 709 INDEXES
757 1.1 INDEX OF APPLICATIONS 757 1.2 INDEX OF ALGORITHMS 759 1.3 INDEX
OF NOTATIONS 761 1.4 GENERAL INDEX 767 |
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| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | Second edition |
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| id | DE-604.BV022951430 |
| illustrated | Illustrated |
| index_date | 2024-07-02T19:02:27Z |
| indexdate | 2024-07-09T21:08:26Z |
| institution | BVB |
| isbn | 158488505X 9781584885054 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016155893 |
| oclc_num | 61458362 |
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| owner_facet | DE-92 DE-634 DE-521 DE-91G DE-BY-TUM DE-83 DE-188 DE-1050 |
| physical | 779 Seiten Ill., graph. Darst. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Chapman & Hall/CRC |
| record_format | marc |
| series2 | Discrete Mathematics and its Applications |
| spelling | Gross, Jonathan L. 1941- Verfasser (DE-588)124283926 aut Graph theory and its applications Jonathan L. Gross, Jay Yellen Second edition Boca Raton, Fla. [u.a.] Chapman & Hall/CRC 2006 779 Seiten Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Discrete Mathematics and its Applications Includes bibliographical references (S. 695-708) and indexes Graphes, Théorie des Matemática discreta larpcal Teoria dos grafos larpcal Graph theory Graphentheorie (DE-588)4113782-6 gnd rswk-swf Graphentheorie (DE-588)4113782-6 s DE-604 Yellen, Jay Verfasser (DE-588)141942878 aut http://www.loc.gov/catdir/toc/fy0602/2005052906.html Table of contents only http://www.loc.gov/catdir/enhancements/fy0647/2005052906-d.html Publisher description HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016155893&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gross, Jonathan L. 1941- Yellen, Jay Graph theory and its applications Graphes, Théorie des Matemática discreta larpcal Teoria dos grafos larpcal Graph theory Graphentheorie (DE-588)4113782-6 gnd |
| subject_GND | (DE-588)4113782-6 |
| title | Graph theory and its applications |
| title_auth | Graph theory and its applications |
| title_exact_search | Graph theory and its applications |
| title_exact_search_txtP | Graph theory and its applications |
| title_full | Graph theory and its applications Jonathan L. Gross, Jay Yellen |
| title_fullStr | Graph theory and its applications Jonathan L. Gross, Jay Yellen |
| title_full_unstemmed | Graph theory and its applications Jonathan L. Gross, Jay Yellen |
| title_short | Graph theory and its applications |
| title_sort | graph theory and its applications |
| topic | Graphes, Théorie des Matemática discreta larpcal Teoria dos grafos larpcal Graph theory Graphentheorie (DE-588)4113782-6 gnd |
| topic_facet | Graphes, Théorie des Matemática discreta Teoria dos grafos Graph theory Graphentheorie |
| url | http://www.loc.gov/catdir/toc/fy0602/2005052906.html http://www.loc.gov/catdir/enhancements/fy0647/2005052906-d.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016155893&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT grossjonathanl graphtheoryanditsapplications AT yellenjay graphtheoryanditsapplications |