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Graph Theory for Operations Research and Management

Book Description

While typically many approaches have been mainly mathematics focused, graph theory has become a tool used by scientists, researchers, and engineers in using modeling techniques to solve real-world problems.

Graph Theory for Operations Research and Management: Applications in Industrial Engineering presents traditional and contemporary applications of graph theory in the areas of industrial engineering, management science, and applied operations research. This comprehensive collection of research introduces the useful basic concepts of graph theory in real world applications.

Table of Contents

  1. Cover
  2. Title Page
  3. Copyright Page
  4. Editorial Advisory Board and List of Reviewers
    1. Editorial Advisory Board
    2. List of Reviewers
  5. Preface
    1. MOTIVATION
    2. ORGANIZATION OF THE BOOK
  6. Acknowledgment
  7. Section 1: Basic Concepts of Graph Theory
    1. Chapter 1: Basics of Graph Theory
      1. ABSTRACT
      2. INTRODUCTION
      3. HISTORICAL BACKGROUND
      4. NOTATION AND TERMINOLOGY
    2. Chapter 2: Matrices
      1. ABSTRACT
      2. INTRODUCTION
      3. DEFINITIONS
      4. ADJACENCY MATRIX
      5. INCIDENCE MATRIX
      6. CYCLE MATRIX
      7. CUT-SET MATRIX
      8. PATH MATRIX
      9. VISUAL SIMILARITY MATRIX
      10. OTHER MATRICES
      11. SUMMARY
      12. APPENDIX
    3. Chapter 3: Isomorphism
      1. ABSTRACT
      2. INTRODUCTION
      3. ISOMORPHISM
      4. LABELING
      5. AUTOMORPHISM
      6. ISOMORPHISM TESTING
      7. CHARACTERISTIC POLYNOMIAL
      8. ISOMORPHISM COMPLEXITY
      9. SUMMARY
    4. Chapter 4: Connectivity
      1. ABSTRACT
      2. INTRODUCTION
      3. CONNECTED GRAPHS
      4. VERTEX AND EDGE CONNECTIVITY
      5. BLOCKS
      6. DIGRAPH CONNECTIVITY
      7. AN APPLICATION: MAKING A ROAD SYSTEM ONE–WAY
      8. CONNECTIVITY SEARCH ALGORITHMS
      9. CONCLUSION
    5. Chapter 5: Trees
      1. ABSTRACT
      2. INTRODUCTION
      3. SPANNING TREE
      4. FUNDAMENTAL CYCLES AND BONDS
      5. ALGORITHMS FOR BRANCHING SEARCH
      6. BINARY TREES
      7. CONCLUSION
    6. Chapter 6: Planarity
      1. ABSTRACT
      2. DEFINITIONS OF PLANE AND PLANAR GRAPHS
      3. BASIC THEOREMS
      4. ALGORITHMS TO RECOGNIZE PLANARITY
      5. DUALITY
      6. THICKNESS AND CROSSING NUMBERS
      7. CONCLUSION
    7. Chapter 7: Eulerian Trails and Tours
      1. ABSTRACT
      2. INTRODUCTION
      3. BACKGROUND
      4. DEFINITIONS AND THEOREMS OF EULERIAN TRAILS AND TOURS
      5. FAMOUS PUZZLES AND APPLICATIONS
      6. COUNTING THE NUMBER OF EULER TOURS (TRAILS)
      7. KOTZIG TRANSFORMATIONS
      8. EULERIAN ORIENTATION
      9. CONCLUSION
    8. Chapter 8: Hamiltonian Paths and Cycles
      1. ABSTRACT
      2. INTRODUCTION
      3. HISTORICAL BACKGROUND
      4. HAMILTONIAN PATHS AND CYCLES
      5. HAMILTONAIN GRAPH PROBLEMS
      6. NECESSARY AND (OR) SUFFICIENT CONDITIONS FOR EXISTENCE OF HAMILTONIAN CYCLE
      7. HAMILTONIAN GRAPHS AND EULERIAN GRAPHS RELATIONSHIP
      8. HAMILTONIAN CYCLE ALGORITHMS
      9. CONCLUSION
    9. Chapter 9: Graph Coloring
      1. ABSTRACT
      2. INTRODUCTION
      3. HISTORICAL BACKGROUND
      4. VERTEX COLORING
      5. EDGE COLORING
      6. CONCLUSION
    10. Chapter 10: Matching Theory
      1. ABSTRACT
      2. INTRODUCTION
      3. APPLICATION OF MATCHING ALGORITHMS IN FAMOUS INDUSTRIAL ENGINEERING PROBLEMS
      4. CONCLUSION
    11. Chapter 11: Digraphs
      1. ABSTRACT
      2. DIGRAPHS AND BASIC DEFINITIONS
      3. CLASSIFICATION OF DIGRAPHS
      4. CONNECTIVITY AND REACHABILITY IN DIGRAPHS
      5. SOME APPLICATIONS OF DIGRAPHS
      6. CONCLUSION
    12. Chapter 12: Networks
      1. ABSTRACT
      2. INTRODUCTION
      3. NETWORK FLOW THEORY
      4. NETWORK FLOW PROBLEMS
      5. ALGORITHMS AND SOLUTION PROCEDURES
      6. CONCLUSION
    13. Chapter 13: Adaptive Network Structures for Data/Text Pattern Recognition (Theory)
      1. ABSTRACT
      2. INTRODUCTION
      3. SEARCH BASED SYSTEMS
      4. LINKAGE BETWEEN ARTIFICIAL NEURAL NETWORKS AND GRAPH THEORY
      5. GRAPH AS INTEGRAL PART OF NEURONAL LEARNING
      6. CONCLUSION
  8. Section 2: Applications
    1. Chapter 14: Inbound Logistics and Vehicle Routing
      1. ABSTRACT
      2. INTRODUCTION
      3. THE TRADITIONAL AGV GUIDE PATH
      4. THE NOVEL ALGORITHM FOR UCFP
    2. Chapter 15: Facility Layout Planning
      1. ABSTRACT
      2. INTRODUCTION
      3. MATHEMATICAL MODELS
      4. CONCLUSION
    3. Chapter 16: Chinese Postman Problem
      1. ABSTRACT
      2. INTRODUCTION
      3. VARIATIONS OF CHINESE POSTMAN PROBLEM
      4. UNDIRECTED CHINESE POSTMAN PROBLEM
    4. Chapter 17: Recovering Drawing Trajectory
      1. ABSTRACT
      2. INTRODUCTION
      3. BACKGROUND
      4. GRAPH-BASED OFFLINE HANDWRITTEN IMAGE RECOGNITION
      5. CONCLUSION
    5. Chapter 18: Higher Education Management
      1. ABSTRACT
      2. CURRICULUM DESIGN
      3. SUMMARY
      4. APPENDIX
    6. Chapter 19: Networks Flow Applications
      1. ABSTRACT
      2. APPLICATIONS OF THE SHORTEST PATH PROBLEM
      3. APPLICATIONS OF THE MAXIMUM FLOW PROBLEM
      4. APPLICATIONS OF THE MINIMUM-COST FLOW PROBLEM
      5. CONCLUSION AND FUTURE TRENDS
    7. Chapter 20: Phasing of Traffic Lights in Urban Intersections
      1. ABSTRACT
      2. INTRODUCTION
      3. VERTEX COLORING APPROACH
      4. CIRCULAR COLORING APPROACH
      5. CONCLUSION
    8. Chapter 21: Train Timetable Construction
      1. ABSTRACT
      2. INTRODUCTION
      3. CONCLUSION
    9. Chapter 22: Industrial and Urban Applications of Eulerian and Chinese Walks
      1. ABSTRACT
      2. INTRODUCTION
      3. INDUSTRIAL MANUFACTURING APPLICATIONS
      4. URBAN APPLICATIONS
      5. CONCLUDING REMARKS
    10. Chapter 23: Adaptive Network Structures for Data/Text Pattern Recognition (Application)
      1. ABSTRACT
      2. INTRODUCTION
      3. DATASETS
      4. DATASET PRE-PROCESSING
      5. DATA PARTITIONING
      6. NEURAL BASED INTELLIGENT AGENT DESIGN
      7. SAMPLE APPLICATIONS OF ARTIFICIAL NEURAL NETWORKS
      8. FUTURE DIRECTIONS
    11. Chapter 24: Understanding Reinforcement Learning Theory for Operations Research and Management
      1. ABSTRACT
      2. INTRODUCTION
      3. LITERATURE REVIEW
      4. REINFORCEMENT LEARNING
      5. MEASUREMENT AND ESTIMATION
      6. CONCLUSION
  9. Compilation of References
  10. About the Contributors