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Graph theory: modeling, applications, and algorithms

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Bibliographic Details
Main Authors:	Agnarsson, Geir (Author), Greenlaw, Raymond (Author)
Format:	Book
Language:	English
Published:	Upper Saddle River, NJ [u.a.] Pearson Education Internat. 2007
Edition:	International ed.
Subjects:	Algorithms Graph theory Graphentheorie
Online Access:	Inhaltsverzeichnis Inhaltsverzeichnis
Item Description:	Literaturverz. S. 431 - 433
Physical Description:	XVII, 446 S. graph. Darst.
ISBN:	0131565362

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adam_text	GRAPH THEORY: MODELING, APPLICATIONS, AND ALGORITHMS GEIR AGNARSSON DEPARTMENT OF MATHEMATICS GEORGE MASON UNIVERSITY RAYMOND GREENLAW SCHOOL OF COMPUTING ARMSTRONG ATLANTIC STATE UNIVERSITY PEARSON PRENTICE HALL PEARSON EDUCATION INTERNATIONAL I PREFACE IX 1 INTRODUCTION TO GRAPH THEORY 1 1.1 INTRODUCTION 1 1.2 WHY STUDY GRAPHS? 1 1.3 MATHEMATICAL PRELIMINARIES 6 1.4 THE DEFINITION OFA GRAPH 10 1.5 EXAMPLES OF COMMON GRAPHS 13 1.6 DEGREES AND REGULAER GRAPHS 15 1.7 SUBGRAPHS 19 1.8 THE DEFINITION OF A DIRECTED GRAPH 21 1.9 INDEGREES AND OUTDEGREES IN A DIGRAPH 24 1.10 EXERCISES 26 2 BASIC CONCEPTS IN GRAPH THEORY 31 2.1 PATHS AND CYCLES 31 2.2 CONNECTIVITY 35 2.3 HOMOMORPHISMS AND TSOMORPHISMS OF GRAPHS 39 2.4 MORE ON ISOMORPHISMS ON SIMPLE GRAPHS 45 2.5 FORMATIONS AND MINORS OF GRAPHS 48 2.6 HOMOMORPHISMS AND ISOMORPHISMS FOR DIGRAPHS 55 2.7 DIGRAPH CONNECTIVITY 58 2.8 EXERCISES 61 3 TREES AND FORESTS 66 3.1 TREES AND SOMEOFTHEIR BASIC PROPERTIES 66 3.2 CHARACTERIZATIONS OF TREES 70 3.3 INDUETIVE PROOFS ON TREES 71 3.4 ERDOES-SZEKERES THEOREM ON SEQUENCES 74 3.5 CENTERS IN TREES 77 3.6 ROOTED TREES 81 3.7 BINARY TREES 83 3.8 EEVELS IN ROOTED AND BINARY TREES 88 3.9 EXERCISES 93 VI CONTENTS 4 SPANNING TREES 98 4.1 SPANNING TREES AND FORESTS 98 4.2 SPANNING TREES OF THE COMPLETE GRAPH 101 4.3 THE ADJACENCY MATRIX OFA GRAPH 104 4.4 THE INCIDENCE MATRIX OFA GRAPH 108 4.5 THE MATRIX-TREE THEOREM 112 4.6 AN APPLICATION TO ELECTRICAL NETWORKS 117 4.7 MINIMUM COST SPANNING TREES 121 4.8 EXERCISES 126 5 FUNDAMENTAL PROPERTIES OF GRAPHS AND DIGRAPHS 132 5.1 BIPARTITE GRAPHS 132 5.2 EULERIAN GRAPHS 135 5.3 HAMILTONIAN GRAPHS 139 5.4 HAMILTONIAN CYCLES IN WEIGHTED GRAPHS 144 5.5 EULERIAN AND HAMILTONIAN DIGRAPHS 145 5.6 TOURNAMENT DIGRAPHS 147 5.7 ON THE ADJACENCY MATRIX OFA DIGRAPH 150 5.8 ACYCLIC DIGRAPHS AND POSETS 152 5.9 EXERCISES 155 6 CONNECTIVITY AND FLOW 160 6.1 EDGECUTS 160 6.2 EDGE CONNECTIVITY AND CONNECTIVITY 163 6.3 BLOCKS IN SEPARABLE GRAPHS 168 6.4 FLOWS IN NETWORKS 173 6.5 THE THEOREMS OF MENGER 185 6.6 EXERCISES 190 7 PLANAR GRAPHS 195 7.1 EMBEDDINGS IN SURFACES 195 7.2 MORE ON PLANAR EMBEDDINGS 199 7.3 EULER S FORMULA AND CONSEQUENCES 201 7.4 CHARACTERIZATION OF PLANAR GRAPHS 205 7.5 KURATOWSKI AND WAGNER S THEOREM 210 7.6 PLANE DUALITY 214 7.7 HIGHER GENUS 220 7.8 GENERALIZATION OF EULER S FORMULA 224 7.9 CROSSING NUMBER 227 7.10 EXERCISES 228 8 GRAPH COLORING 232 8.1 THE CHROMATIC NUMBER OF A GRAPH 232 8.2 MULTIPARTITE GRAPHS 236 8.3 RESULTS FOR GENERAL GRAPHS 241 8.4 PLANAR GRAPHS AND OTHER SURFACE GRAPHS 245 8.5 EDGE COLORING OF A GRAPH 252 CONTENTS VUE 8.6 TAIT S THEOREM 257 8.7 EXERCISES 259 9 COLORING ENUMERATIONS AND CHORDAL GRAPHS 267 9. 1 THE CHROMATIC POLYNOMIAL OF A GRAPH 267 9.2 BASIC PROPERTIES OF THE CHROMATIC POLYNOMIAL 272 9.3 INTERVAL AND TNTERSECTION GRAPHS 275 9.4 CHORDAL GRAPHS 284 9.5 POWERS OF GRAPHS 290 9.6 EXERCISES 296 10 INDEPENDENCE, DOMINANCE, AND MATCHINGS 299 10.1 INDEPENDENCE OF VERTICES 299 10.2 DOMINATION OF VERTICES 305 10.3 MATCHINGS IN A GRAPH 312 10.4 HALL S MARRIAGE THEOREM 318 10.5 EXERCISES 323 11 COVER PARAMETERS AND MATCHING POLYNOMIALS 327 1 ] . 1 COVERS AND RELATED PARAMETERS 327 11.2 ROOK POLYNOMIALS AND BIPARTITE GRAPHS 333 11.3 THE MATCHING DEFECT POLYNOMIAL 340 11.4 MATCHING ALGORITHMS 343 11.5 EXERCISES 351 12 GRAPH COUNTING 356 12.1 TNTRODUCTION 356 1.2.2 BASIC COUNTING RESULTS 358 12.3 GENERATING FUNCTIONS 365 12.4 PARTITIONS OF A FINITE SET 371 12.5 THE LABCLED COUNTING LEMMA 374 J2.6 THE EXPONENTIAL FORMULA 378 12.7 THE NUMHER TWO AND RELATED GRAPHS 381 12.7.1 TWO-REGULAR GRAPHS 381 12.7.2 TWO-COLORABLE GRAPHS 382 12.7.3 EVEN GRAPHS 384 12.8 EXERCISES 386 13 GRAPH ALGORITHMS 392 13.1 LNTRODUCTION 392 13.2 RCCAP OF ALGORITHMS ALREADY PRESENTED 393 13.3 ALGORITHM EFFICIENCY 394 13.4 BREADTH-FIRST SEARCH 396 13.5 DEPTH-FIRST SEARCH 400 13.6 CONNECTED COMPONENTS 403 13.7 DIJKSTRA S SHORTEST PATH ALGORITHM 407 13.8 JAVA SOURCE CODE 411 13.9 EXERCISES 416 VIII CONTENTS APPENDICES A GREEK ALPHABET 421 B NOTATION 423 C TOP TEN ONLINE REFERENCES 429 BIBLIOGRAPHY 431 INDEX 435
adam_txt	GRAPH THEORY: MODELING, APPLICATIONS, AND ALGORITHMS GEIR AGNARSSON DEPARTMENT OF MATHEMATICS GEORGE MASON UNIVERSITY RAYMOND GREENLAW SCHOOL OF COMPUTING ARMSTRONG ATLANTIC STATE UNIVERSITY PEARSON PRENTICE HALL PEARSON EDUCATION INTERNATIONAL I PREFACE IX 1 INTRODUCTION TO GRAPH THEORY 1 1.1 INTRODUCTION 1 1.2 WHY STUDY GRAPHS? 1 1.3 MATHEMATICAL PRELIMINARIES 6 1.4 THE DEFINITION OFA GRAPH 10 1.5 EXAMPLES OF COMMON GRAPHS 13 1.6 DEGREES AND REGULAER GRAPHS 15 1.7 SUBGRAPHS 19 1.8 THE DEFINITION OF A DIRECTED GRAPH 21 1.9 INDEGREES AND OUTDEGREES IN A DIGRAPH 24 1.10 EXERCISES 26 2 BASIC CONCEPTS IN GRAPH THEORY 31 2.1 PATHS AND CYCLES 31 2.2 CONNECTIVITY 35 2.3 HOMOMORPHISMS AND TSOMORPHISMS OF GRAPHS 39 2.4 MORE ON ISOMORPHISMS ON SIMPLE GRAPHS 45 2.5 FORMATIONS AND MINORS OF GRAPHS 48 2.6 HOMOMORPHISMS AND ISOMORPHISMS FOR DIGRAPHS 55 2.7 DIGRAPH CONNECTIVITY 58 2.8 EXERCISES 61 3 TREES AND FORESTS 66 3.1 TREES AND SOMEOFTHEIR BASIC PROPERTIES 66 3.2 CHARACTERIZATIONS OF TREES 70 3.3 INDUETIVE PROOFS ON TREES 71 3.4 ERDOES-SZEKERES THEOREM ON SEQUENCES 74 3.5 CENTERS IN TREES 77 3.6 ROOTED TREES 81 3.7 BINARY TREES 83 3.8 EEVELS IN ROOTED AND BINARY TREES 88 3.9 EXERCISES 93 VI CONTENTS 4 SPANNING TREES 98 4.1 SPANNING TREES AND FORESTS 98 4.2 SPANNING TREES OF THE COMPLETE GRAPH 101 4.3 THE ADJACENCY MATRIX OFA GRAPH 104 4.4 THE INCIDENCE MATRIX OFA GRAPH 108 4.5 THE MATRIX-TREE THEOREM 112 4.6 AN APPLICATION TO ELECTRICAL NETWORKS 117 4.7 MINIMUM COST SPANNING TREES 121 4.8 EXERCISES 126 5 FUNDAMENTAL PROPERTIES OF GRAPHS AND DIGRAPHS 132 5.1 BIPARTITE GRAPHS 132 5.2 EULERIAN GRAPHS 135 5.3 HAMILTONIAN GRAPHS 139 5.4 HAMILTONIAN CYCLES IN WEIGHTED GRAPHS 144 5.5 EULERIAN AND HAMILTONIAN DIGRAPHS 145 5.6 TOURNAMENT DIGRAPHS 147 5.7 ON THE ADJACENCY MATRIX OFA DIGRAPH 150 5.8 ACYCLIC DIGRAPHS AND POSETS 152 5.9 EXERCISES 155 6 CONNECTIVITY AND FLOW 160 6.1 EDGECUTS 160 6.2 EDGE CONNECTIVITY AND CONNECTIVITY 163 6.3 BLOCKS IN SEPARABLE GRAPHS 168 6.4 FLOWS IN NETWORKS 173 6.5 THE THEOREMS OF MENGER 185 6.6 EXERCISES 190 7 PLANAR GRAPHS 195 7.1 EMBEDDINGS IN SURFACES 195 7.2 MORE ON PLANAR EMBEDDINGS 199 7.3 EULER'S FORMULA AND CONSEQUENCES 201 7.4 CHARACTERIZATION OF PLANAR GRAPHS 205 7.5 KURATOWSKI AND WAGNER'S THEOREM 210 7.6 PLANE DUALITY 214 7.7 HIGHER GENUS 220 7.8 GENERALIZATION OF EULER'S FORMULA 224 7.9 CROSSING NUMBER 227 7.10 EXERCISES 228 8 GRAPH COLORING 232 8.1 THE CHROMATIC NUMBER OF A GRAPH 232 8.2 MULTIPARTITE GRAPHS 236 8.3 RESULTS FOR GENERAL GRAPHS 241 8.4 PLANAR GRAPHS AND OTHER SURFACE GRAPHS 245 8.5 EDGE COLORING OF A GRAPH 252 CONTENTS VUE 8.6 TAIT'S THEOREM 257 8.7 EXERCISES 259 9 COLORING ENUMERATIONS AND CHORDAL GRAPHS 267 9. 1 THE CHROMATIC POLYNOMIAL OF A GRAPH 267 9.2 BASIC PROPERTIES OF THE CHROMATIC POLYNOMIAL 272 9.3 INTERVAL AND TNTERSECTION GRAPHS 275 9.4 CHORDAL GRAPHS 284 9.5 POWERS OF GRAPHS 290 9.6 EXERCISES 296 10 INDEPENDENCE, DOMINANCE, AND MATCHINGS 299 10.1 INDEPENDENCE OF VERTICES 299 10.2 DOMINATION OF VERTICES 305 10.3 MATCHINGS IN A GRAPH 312 10.4 HALL'S MARRIAGE THEOREM 318 10.5 EXERCISES 323 11 COVER PARAMETERS AND MATCHING POLYNOMIALS 327 1 ] . 1 COVERS AND RELATED PARAMETERS 327 11.2 ROOK POLYNOMIALS AND BIPARTITE GRAPHS 333 11.3 THE MATCHING DEFECT POLYNOMIAL 340 11.4 MATCHING ALGORITHMS 343 11.5 EXERCISES 351 12 GRAPH COUNTING 356 12.1 TNTRODUCTION 356 1.2.2 BASIC COUNTING RESULTS 358 12.3 GENERATING FUNCTIONS 365 12.4 PARTITIONS OF A FINITE SET 371 12.5 THE LABCLED COUNTING LEMMA 374 J2.6 THE EXPONENTIAL FORMULA 378 12.7 THE NUMHER TWO AND RELATED GRAPHS 381 12.7.1 TWO-REGULAR GRAPHS 381 12.7.2 TWO-COLORABLE GRAPHS 382 12.7.3 EVEN GRAPHS 384 12.8 EXERCISES 386 13 GRAPH ALGORITHMS 392 13.1 LNTRODUCTION 392 13.2 RCCAP OF ALGORITHMS ALREADY PRESENTED 393 13.3 ALGORITHM EFFICIENCY 394 13.4 BREADTH-FIRST SEARCH 396 13.5 DEPTH-FIRST SEARCH 400 13.6 CONNECTED COMPONENTS 403 13.7 DIJKSTRA'S SHORTEST PATH ALGORITHM 407 13.8 JAVA SOURCE CODE 411 13.9 EXERCISES 416 VIII CONTENTS APPENDICES A GREEK ALPHABET 421 B NOTATION 423 C TOP TEN ONLINE REFERENCES 429 BIBLIOGRAPHY 431 INDEX 435
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spellingShingle	Agnarsson, Geir Greenlaw, Raymond Graph theory modeling, applications, and algorithms Algorithms Graph theory Graphentheorie (DE-588)4113782-6 gnd
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title	Graph theory modeling, applications, and algorithms
title_auth	Graph theory modeling, applications, and algorithms
title_exact_search	Graph theory modeling, applications, and algorithms
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title_full	Graph theory modeling, applications, and algorithms Geir Agnarsson ; Raymond Greenlaw
title_fullStr	Graph theory modeling, applications, and algorithms Geir Agnarsson ; Raymond Greenlaw
title_full_unstemmed	Graph theory modeling, applications, and algorithms Geir Agnarsson ; Raymond Greenlaw
title_short	Graph theory
title_sort	graph theory modeling applications and algorithms
title_sub	modeling, applications, and algorithms
topic	Algorithms Graph theory Graphentheorie (DE-588)4113782-6 gnd
topic_facet	Algorithms Graph theory Graphentheorie
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