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Graph theory and its applications:

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Bibliographische Detailangaben
Beteiligte Personen:	Gross, Jonathan L. 1941- (VerfasserIn), Yellen, Jay (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Boca Raton, Fla. [u.a.] Chapman & Hall/CRC 2006
Ausgabe:	Second edition
Schriftenreihe:	Discrete Mathematics and its Applications
Schlagwörter:	Graphes, Théorie des Matemática discreta Teoria dos grafos Graph theory Graphentheorie
Links:	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
Beschreibung:	Includes bibliographical references (S. 695-708) and indexes
Umfang:	779 Seiten Ill., graph. Darst.
ISBN:	158488505X 9781584885054

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Datensatz im Suchindex

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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
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author	Gross, Jonathan L. 1941- Yellen, Jay
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illustrated	Illustrated
indexdate	2024-12-20T13:06:04Z
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isbn	158488505X 9781584885054
language	English
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physical	779 Seiten Ill., graph. Darst.
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publisher	Chapman & Hall/CRC
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series2	Discrete Mathematics and its Applications
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_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
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