Graph theory and interconnection networks:
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| Main Authors: | , |
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| Format: | Book |
| Language: | English |
| Published: |
Boca Raton, Fla.[u.a.]
CRC Press
2009
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 706 S. graph. Darst. |
| ISBN: | 1420044818 9781420044812 |
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| adam_text | GRAPH THEORY AND INTERCONNECTION NETWORKS LIH-HSING HSU AND CHENG-KUAN
LIN @ CRC PRESS TAYLOR & FRANCIS GROUP BOCA RATON LONDON NEW YORK CRC
PRESS IS AN IMPRINT OF THE TAYLOR & FRANCIS GROUP, AN INFORMA BUSINESS
CONTENTS PREFACE XI AUTHORS XIII CHAPTER 1: FUNDAMENTAL CONCEPTS 1 1.1
GRAPHS AND SIMPLE GRAPHS 1 1.2 MATRICES AND ISOMORPHISMS 5 1.3 PATHS AND
CYCLES 9 1.4 VERTEX DEGREES 12 1.5 GRAPH OPERATIONS 14 1.6 SOME BASIC
TECHNIQUES 16 1.7 DEGREE SEQUENCES 18 CHAPTER 2: APPLICATIONS ON GRAPH
ISOMORPHISMS 21 2.1 GENERALIZED HONEYCOMB TORI 21 2.2 ISOMORPHISM
BETWEEN CYCLIC-CUBES AND WRAPPED BUTTERFLY NETWORKS 24 2.3 1 -EDGE
FAULT-TOLERANT DESIGN FOR MESHES 26 2.4 FAITHFUL 1-EDGE FAULT-TOLERANT
GRAPHS 31 2.5 AE-EDGE FAULT-TOLERANT DESIGNS FOR HYPERCUBES 40 CHAPTER 3:
DISTANCE AND DIAMETER 43 3.1 INTRODUCTION 43 3.2 DIAMETER FOR SOME
INTERCONNECTION NETWORKS 43 3.3 SHUFFLE-CUBES 47 3.3.1 ROUTEL(U, V) 49
3.4 MOORE BOUND 50 3.5 STAR GRAPHS AND PANCAKE GRAPHS 52 3.6 EDGE
CONGESTION AND BISECTION WIDTH 55 3.7 TRANSMITTING PROBLEM 57 CHAPTER 4:
TREES 61 4.1 BASIC PROPERTIES 61 4.2 BREADTH-FIRST SEARCH AND
DEPTH-FIRST SEARCH 64 4.3 ROOTED TREES 65 4.4 COUNTING TREES 68 4.5
COUNTING BINARY TREES 72 4.6 NUMBER OF SPANNING TREES CONTAINS A CERTAIN
EDGE 73 4.7 EMBEDDING PROBLEM 76 V VI CONTENTS CHAPTER 5: EULERIAN
GRAPHS AND DIGRAPHS 79 5.1 EULERIAN GRAPHS 79 5.2 EULERIAN DIGRAPHS 82
5.3 APPLICATIONS 85 5.3.1 CHINESE POSTMAN PROBLEM 85 5.3.2
STREET-SWEEPING PROBLEM 86 5.3.3 DRUM DESIGN PROBLEM 86 5.3.4 FUNCTIONAL
CELL LAYOUT PROBLEM 87 CHAPTER 6: MATCHINGS AND FACTORS 93 6.1 MATCHINGS
93 6.2 BIPARTITE MATCHING 95 6.3 EDGE COVER 98 6.4 PERFECT MATCHING 100
6.5 FACTORS 103 CHAPTER 7: CONNECTIVITY 105 7.1 CUT AND CONNECTIVITY 105
7.2 2-CONNECTED GRAPHS 109 7.3 MENGER THEOREM ILL 7.4 AN
APPLICATION*MAKING A ROAD SYSTEM ONE-WAY 115 7.5 CONNECTIVITY OF SOME
INTERCONNECTION NETWORKS 117 7.6 WIDE DIAMETERS AND FAULT DIAMETERS 118
7.7 SUPERCONNECTIVITY AND SUPER-EDGE-CONNECTIVITY 120 CHAPTER 8: GRAPH
COLORING 125 8.1 VERTEX COLORINGS AND BOUNDS 125 8.2 PROPERTIES OF
^-CRITICAL GRAPHS 126 8.3 BOUND FOR CHROMATIC NUMBERS 128 8.4 GIRTH AND
CHROMATIC NUMBER 130 8.5 HAJOS CONJECTURE 131 8.6 ENUMERATIVE ASPECTS
133 8.7 HOMOMORPHISM FUNCTIONS 136 8.8 AN APPLICATION*TESTING ON PRINTED
CIRCUIT BOARDS 137 8.9 EDGE-COLORINGS 138 CHAPTER 9: HAMILTONIAN CYCLES
141 9.1 HAMILTONIAN GRAPHS 141 9.2 NECESSARY CONDITIONS 141 9.3
SUFFICIENT CONDITIONS 143 9.4 HAMILTONIAN-CONNECTED 147 9.5 MUTUALLY
INDEPENDENT HAMILTONIAN PATHS 152 9.6 DIAMETER FOR GENERALIZED
SHUFFLE-CUBES 155 9.7 CYCLES IN DIRECTED GRAPHS 158 CONTENTS VII CHAPTER
10: PLANAR GRAPHS 161 10.1 PLANAR EMBEDDINGS 161 10.2 EULER S FORMULA
165 10.3 CHARACTERIZATION OF PLANAR GRAPHS 166 10.4 COLORING OF PLANAR
GRAPHS 167 CHAPTER 11: OPTIMAL &-FAULT-TOLERANT HAMILTONIAN GRAPHS 171
11.1 INTRODUCTION 171 11.2 NODE EXPANSION 173 11.3 OTHER CONSTRUCTION
METHODS 180 11.4 FAULT-TOLERANT HAMILTONICITY AND FAULT-TOLERANT
HAMILTONIAN CONNECTIVITY OF THE FOLDED PETERSEN CUBE NETWORKS 185 11.5
FAULT-TOLERANT HAMILTONICITY AND FAULT-TOLERANT HAMILTONIAN CONNECTIVITY
OF THE PANCAKE GRAPHS 189 11.6 FAULT-TOLERANT HAMILTONICITY AND
FAULT-TOLERANT HAMILTONIAN CONNECTIVITY OF AUGMENTED CUBES 195 11.7
FAULT-TOLERANT HAMILTONICITY AND FAULT-TOLERANT HAMILTONIAN CONNECTIVITY
OF THE WK-RECURSIVE NETWORKS 206 11.8 FAULT-TOLERANT HAMILTONICITY OF
THE FULLY CONNECTED CUBIC NETWORKS 221 CHAPTER 12: OPTIMAL
1-FAULT-TOLERANT HAMILTONIAN GRAPHS 227 12.1 INTRODUCTION 227 12.2
3-JOIN 228 12.3 CYCLE EXTENSION 229 12.4 CELLS FOR OPTIMAL 1
-HAMILTONIAN REGULAR GRAPHS 241 12.5 GENERALIZED PETERSEN GRAPHS 249
12.6 HONEYCOMB RECTANGULAR DISKS 259 12.7 PROPERTIES WITH RESPECT TO THE
3-JOIN 262 12.8 EXAMPLES OF VARIOUS CUBIC PLANAR HAMILTONIAN GRAPHS 267
12.8.1 * * * * * 268 12.8.2 ** * ** 268 12.8.3 * * * * * 268 12.8.4
***** 269 12.8.5 ***** 271 12.8.6 ***** 272 12.8.7 * *|** 273 12.8.8
*~*~** * 274 12.9 HAMILTONIAN PROPERTIES OF DOUBLE LOOP NETWORKS 275
CHAPTER 13: OPTIMAL &-FAULT-TOLERANT HAMILTONIAN-LACEABLE GRAPHS 285
13.1 INTRODUCTION 285 13.2 SUPER FAULT-TOLERANT HAMILTONIAN LACEABILITY
OF HYPERCUBES 287 13.3 SUPER FAULT-TOLERANT HAMILTONIAN LACEABILITY OF
STAR GRAPHS 289 VIII CONTENTS 13.4 CONSTRUCTION SCHEMES 294 13.5 CUBIC
HAMILTONIAN-LACEABLE GRAPHS 301 13.6 LP-FAULT-TOLERANT HAMILTONIAN
GRAPHS 303 13.6.1 SPIDER-WEB NETWORKS 303 13.6.2 BROTHER TREES 312 13.7
HAMILTONIAN LACEABILITY OF FAULTY HYPERCUBES 318 13.8 CONDITIONAL FAULT
HAMILTONICITY AND CONDITIONAL FAULT HAMILTONIAN LACEABILITY OF THE STAR
GRAPHS 327 CHAPTER 14: SPANNING CONNECTIVITY 339 14.1 INTRODUCTION 339
14.2 SPANNING CONNECTIVITY OF GENERAL GRAPHS 339 14.3 SPANNING
CONNECTIVITY AND SPANNING LACEABILITY OF THE HYPERCUBE-LIKE NETWORKS 347
14.4 SPANNING CONNECTIVITY OF CROSSED CUBES 361 14.5 SPANNING
CONNECTIVITY AND SPANNING LACEABILITY OF THE ENHANCED HYPERCUBE NETWORKS
374 14.6 SPANNING CONNECTIVITY OF THE PANCAKE GRAPHS 391 14.7 SPANNING
LACEABILITY OF THE STAR GRAPHS 404 14.8 SPANNING FAN-CONNECTIVITY AND
SPANNING PIPE-CONNECTIVITY OF GRAPHS 410 CHAPTER 15: CUBIC 3*-CONNECTED
GRAPHS AND CUBIC 3*-LACEABLE GRAPHS 417 15.1 PROPERTIES OF CUBIC
3*-CONNECTED GRAPHS 417 15.2 EXAMPLES OF CUBIC SUPER 3*-CONNECTED GRAPHS
419 15.3 COUNTEREXAMPLES OF 3*-CONNECTED GRAPHS 426 15.4 PROPERTIES OF
CUBIC 3*-LACEABLE GRAPHS 430 15.5 EXAMPLES OF CUBIC HYPER 3*-LACEABLE
GRAPHS 431 15.6 COUNTEREXAMPLES OF 3*-LACEABLE GRAPHS 447 CHAPTER 16:
SPANNING DIAMETER 449 16.1 INTRODUCTION 449 16.2 SPANNING DIAMETER FOR
THE STAR GRAPHS 449 16.3 SPANNING DIAMETER OF HYPERCUBES 465 16.4
SPANNING DIAMETER FOR SOME (N, )-STAR GRAPHS 474 CHAPTER 17: PANCYCLIC
AND PANCONNECTED PROPERTY 479 17.1 INTRODUCTION 479 17.2 BIPANCONNECTED
AND BIPANCYCLIC PROPERTIES OF HYPERCUBES 480 17.3 EDGE FAULT-TOLERANT
BIPANCYCLIC PROPERTIES OF HYPERCUBES 485 17.4 PANCONNECTED AND PANCYCLIC
PROPERTIES OF AUGMENTED CUBES 489 17.5 COMPARISON BETWEEN PANCONNECTED
AND PANPOSITIONABLE HAMILTONIAN ... 500 17.6 BIPANPOSITIONABLE
BIPANCYCLIC PROPERTY OF HYPERCUBE 504 CONTENTS IX CHAPTER 18: MUTUALLY
INDEPENDENT HAMILTONIAN CYCLES 509 18.1 INTRODUCTION 509 18.2 MUTUALLY
INDEPENDENT HAMILTONIAN CYCLES ON SOME GRAPHS 510 18.3 MUTUALLY
INDEPENDENT HAMILTONIAN CYCLES OF HYPERCUBES 512 18.4 MUTUALLY
INDEPENDENT HAMILTONIAN CYCLES OF PANCAKE GRAPHS 518 18.5 MUTUALLY
INDEPENDENT HAMILTONIAN CYCLES OF STAR GRAPHS 524 18.6 FAULT-FREE
MUTUALLY INDEPENDENT HAMILTONIAN CYCLES IN A FAULTY HYPERCUBE 526 18.7
FAULT-FREE MUTUALLY INDEPENDENT HAMILTONIAN CYCLES IN FAULTY STAR GRAPHS
530 18.8 ORTHOGONALITY FOR SETS OF MUTUALLY INDEPENDENT HAMILTONIAN
CYCLES 543 CHAPTER 19: MUTUALLY INDEPENDENT HAMILTONIAN PATHS 545 19.1
INTRODUCTION 545 19.2 MUTUALLY INDEPENDENT HAMILTONIAN LACEABILITY FOR
HYPERCUBES 545 19.3 MUTUALLY INDEPENDENT HAMILTONIAN LACEABILITY FOR
STAR GRAPHS 550 19.4 MUTUALLY INDEPENDENT HAMILTONIAN CONNECTIVITY FOR
(N, &)-STAR GRAPHS 555 19.5 CUBIC 2-INDEPENDENT HAMILTONIAN-CONNECTED
GRAPHS 575 19.5.1 EXAMPLES OF CUBIC 2-INDEPENDENT HAMILTONIAN-CONNECTED
GRAPHS THAT ARE SUPER 3*-CONNECTED 576 19.5.2 EXAMPLES OF SUPER
3*-CONNECTED GRAPHS THAT ARE NOT CUBIC 2-INDEPENDENT
HAMILTONIAN-CONNECTED 579 19.5.3 EXAMPLE OF A CUBIC 2-INDEPENDENT
HAMILTONIAN- CONNECTED GRAPH THAT IS NOT SUPER 3*-CONNECTED 580 19.5.4
EXAMPLE OF A CUBIC 1-FAULT-TOLERANT HAMILTONIAN GRAPH THAT IS
HAMILTONIAN-CONNECTED BUT NOT CUBIC 2-INDEPENDENT HAMILTONIAN-CONNECTED
OR SUPER 3*-CONNECTED 581 CHAPTER 20: TOPOLOGICAL PROPERTIES OF
BUTTERFLY GRAPHS 585 20.1 INTRODUCTION 585 20.2 CYCLE EMBEDDING IN
FAULTY BUTTERFLY GRAPHS 590 20.3 SPANNING CONNECTIVITY FOR BUTTERFLY
GRAPHS 607 20.4 MUTUALLY INDEPENDENT HAMILTONICITY FOR BUTTERFLY GRAPHS
616 CHAPTER 21 : DIAGNOSIS OF MULTIPROCESSOR SYSTEMS 625 21.1
INTRODUCTION 625 21.2 DIAGNOSIS MODELS 625 21.2.1 PMC MODEL 626 21.2.2
COMPARISON MODEL 628 21.3 DIAGNOSABILITY OF THE MATCHING COMPOSITION
NETWORKS 631 21.3.1 DIAGNOSABILITY OF THE MATCHING COMPOSITION NETWORKS
UNDER THE PMC MODEL 632 X CONTENTS 21.3.2 DIAGNOSABILITY OF THE MATCHING
COMPOSITION NETWORKS UNDER THE COMPARISON MODEL 632 21.4 DIAGNOSABILITY
OF CARTESIAN PRODUCT NETWORKS , 637 21.4.1 DIAGNOSABILITY OF CARTESIAN
PRODUCT NETWORKS UNDER THE PMC MODEL 638 21.4.2 DIAGNOSABILITY OF
CARTESIAN PRODUCT NETWORKS UNDER THE COMPARISON MODEL 639 21.4.3
DIAGNOSABILITY OF F-CONNECTED NETWORKS 639 21.4.4 DIAGNOSABILITY OF
HOMOGENEOUS PRODUCT NETWORKS 641 21.4.5 DIAGNOSABILITY OF HETEROGENEOUS
PRODUCT NETWORKS 644 21.5 STRONGLY ?-DIAGNOSABLE SYSTEMS 645 21.5.1
STRONGLY *-DIAGNOSABLE SYSTEMS IN THE MATCHING COMPOSITION NETWORKS 649
21.6 CONDITIONAL DIAGNOSABILITY 652 21.6.1 CONDITIONAL DIAGNOSABILITY OF
Q N UNDER THE PMC MODEL 653 21.7 CONDITIONAL DIAGNOSABILITY OF Q* UNDER
THE COMPARISON MODEL 658 21.7.1 CONDITIONAL DIAGNOSABILITY OF CAYLEY
GRAPHS GENERATED BY TRANSPOSITION TREES UNDER THE COMPARISON DIAGNOSIS
MODEL 666 21.7.2 CAYLEY GRAPHS GENERATED BY TRANSPOSITION TREES 666
21.7.3 CONDITIONAL DIAGNOSABILITY 668 21.8 LOCAL DIAGNOSABILITY 670
21.8.1 STRONGLY LOCAL-DIAGNOSABLE PROPERTY 675 21.8.2 CONDITIONAL FAULT
LOCAL DIAGNOSABILITY 679 REFERENCES 687 INDEX 703
|
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| id | DE-604.BV035878409 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:06:37Z |
| institution | BVB |
| isbn | 1420044818 9781420044812 |
| language | English |
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| physical | XIII, 706 S. graph. Darst. |
| publishDate | 2009 |
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| spelling | Hsu, Lih-Hsing Verfasser aut Graph theory and interconnection networks Lih-Hsing Hsu and Cheng-Kuan Lin Boca Raton, Fla.[u.a.] CRC Press 2009 XIII, 706 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematisches Modell Interconnects (Integrated circuit technology) / Design and construction Interconnects (Integrated circuit technology) / Mathematical models Graph theory Lin, Cheng-Kuan Verfasser aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018736038&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hsu, Lih-Hsing Lin, Cheng-Kuan Graph theory and interconnection networks Mathematisches Modell Interconnects (Integrated circuit technology) / Design and construction Interconnects (Integrated circuit technology) / Mathematical models Graph theory |
| title | Graph theory and interconnection networks |
| title_auth | Graph theory and interconnection networks |
| title_exact_search | Graph theory and interconnection networks |
| title_full | Graph theory and interconnection networks Lih-Hsing Hsu and Cheng-Kuan Lin |
| title_fullStr | Graph theory and interconnection networks Lih-Hsing Hsu and Cheng-Kuan Lin |
| title_full_unstemmed | Graph theory and interconnection networks Lih-Hsing Hsu and Cheng-Kuan Lin |
| title_short | Graph theory and interconnection networks |
| title_sort | graph theory and interconnection networks |
| topic | Mathematisches Modell Interconnects (Integrated circuit technology) / Design and construction Interconnects (Integrated circuit technology) / Mathematical models Graph theory |
| topic_facet | Mathematisches Modell Interconnects (Integrated circuit technology) / Design and construction Interconnects (Integrated circuit technology) / Mathematical models Graph theory |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018736038&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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