Handbook of Product Graphs, 2nd Edition

Book description

Handbook of Product Graphs, Second Edition examines the dichotomy between the structure of products and their subgraphs. It also features the design of efficient algorithms that recognize products and their subgraphs and explores the relationship between graph parameters of the product and factors. Extensively revised and expanded, the handbook pre

Table of contents

  1. Front Cover (1/2)
  2. Front Cover (2/2)
  3. Contents (1/2)
  4. Contents (2/2)
  5. Foreword
  6. Preface
  7. I. A Brief Introduction to Graphs and Their Products
    1. 1. Graphs (1/2)
    2. 1. Graphs (2/2)
    3. 2. Automorphisms and Invariants (1/3)
    4. 2. Automorphisms and Invariants (2/3)
    5. 2. Automorphisms and Invariants (3/3)
    6. 3. Hypercubes and Isometric Subgraphs (1/2)
    7. 3. Hypercubes and Isometric Subgraphs (2/2)
    8. 4. Graph Products (1/3)
    9. 4. Graph Products (2/3)
    10. 4. Graph Products (3/3)
    11. 5. The Four Standard Graph Products (1/3)
    12. 5. The Four Standard Graph Products (2/3)
    13. 5. The Four Standard Graph Products (3/3)
  8. II. Factorization and Cancellation
    1. 6. Cartesian Product (1/3)
    2. 6. Cartesian Product (2/3)
    3. 6. Cartesian Product (3/3)
    4. 7. Strong Product (1/2)
    5. 7. Strong Product (2/2)
    6. 8. Direct Product (1/4)
    7. 8. Direct Product (2/4)
    8. 8. Direct Product (3/4)
    9. 8. Direct Product (4/4)
    10. 9. Cancellation (1/2)
    11. 9. Cancellation (2/2)
    12. 10. Lexicographic Product (1/4)
    13. 10. Lexicographic Product (2/4)
    14. 10. Lexicographic Product (3/4)
    15. 10. Lexicographic Product (4/4)
  9. III. Isometric Embeddings
    1. 11. The Relation Θ and Partial Cubes (1/2)
    2. 11. The Relation Θ and Partial Cubes (2/2)
    3. 12. Median Graphs (1/3)
    4. 12. Median Graphs (2/3)
    5. 12. Median Graphs (3/3)
    6. 13. The Canonical Isometric Embedding (1/2)
    7. 13. The Canonical Isometric Embedding (2/2)
    8. 14. A Dynamic Location Problem (1/4)
    9. 14. A Dynamic Location Problem (2/4)
    10. 14. A Dynamic Location Problem (3/4)
    11. 14. A Dynamic Location Problem (4/4)
    12. 15. Isometries in Strong Products and Product Dimensions (1/2)
    13. 15. Isometries in Strong Products and Product Dimensions (2/2)
    14. 16. Fixed Box Theorems (1/2)
    15. 16. Fixed Box Theorems (2/2)
  10. IV. Algorithms
    1. 17. Graph Representation and Algorithms (1/2)
    2. 17. Graph Representation and Algorithms (2/2)
    3. 18. Recognizing Hypercubes and Partial Cubes (1/3)
    4. 18. Recognizing Hypercubes and Partial Cubes (2/3)
    5. 18. Recognizing Hypercubes and Partial Cubes (3/3)
    6. 19. Chemical Graphs and the Wiener Index (1/2)
    7. 19. Chemical Graphs and the Wiener Index (2/2)
    8. 20. Arboricity, Squares, and Triangles (1/2)
    9. 20. Arboricity, Squares, and Triangles (2/2)
    10. 21. Recognizing Median Graphs (1/4)
    11. 21. Recognizing Median Graphs (2/4)
    12. 21. Recognizing Median Graphs (3/4)
    13. 21. Recognizing Median Graphs (4/4)
    14. 22. Recognizing Partial Hamming Graphs and Quasi-Median Graphs (1/2)
    15. 22. Recognizing Partial Hamming Graphs and Quasi-Median Graphs (2/2)
    16. 23. Factoring the Cartesian Product (1/3)
    17. 23. Factoring the Cartesian Product (2/3)
    18. 23. Factoring the Cartesian Product (3/3)
    19. 24. Recognizing Direct, Strong, and Lexicographic Products (1/3)
    20. 24. Recognizing Direct, Strong, and Lexicographic Products (2/3)
    21. 24. Recognizing Direct, Strong, and Lexicographic Products (3/3)
  11. V. Invariants
    1. 25. Connectivity (1/2)
    2. 25. Connectivity (2/2)
    3. 26. Coloring and Hedetniemi's Conjecture (1/5)
    4. 26. Coloring and Hedetniemi's Conjecture (2/5)
    5. 26. Coloring and Hedetniemi's Conjecture (3/5)
    6. 26. Coloring and Hedetniemi's Conjecture (4/5)
    7. 26. Coloring and Hedetniemi's Conjecture (5/5)
    8. 27. Independence Number and Shannon Capacity (1/3)
    9. 27. Independence Number and Shannon Capacity (2/3)
    10. 27. Independence Number and Shannon Capacity (3/3)
    11. 28. Domination and Vizing's Conjecture (1/3)
    12. 28. Domination and Vizing's Conjecture (2/3)
    13. 28. Domination and Vizing's Conjecture (3/3)
    14. 29. Cycle Spaces and Bases (1/2)
    15. 29. Cycle Spaces and Bases (2/2)
    16. 30. Selected Results (1/4)
    17. 30. Selected Results (2/4)
    18. 30. Selected Results (3/4)
    19. 30. Selected Results (4/4)
  12. VI. Related Concepts
    1. 31. Infinite Graphs (1/5)
    2. 31. Infinite Graphs (2/5)
    3. 31. Infinite Graphs (3/5)
    4. 31. Infinite Graphs (4/5)
    5. 31. Infinite Graphs (5/5)
    6. 32. Products of Digraphs (1/2)
    7. 32. Products of Digraphs (2/2)
    8. 33. Near Products (1/3)
    9. 33. Near Products (2/3)
    10. 33. Near Products (3/3)
  13. Appendix: Hints and Solutions to Exercises (1/5)
  14. Appendix: Hints and Solutions to Exercises (2/5)
  15. Appendix: Hints and Solutions to Exercises (3/5)
  16. Appendix: Hints and Solutions to Exercises (4/5)
  17. Appendix: Hints and Solutions to Exercises (5/5)
  18. Bibliography (1/7)
  19. Bibliography (2/7)
  20. Bibliography (3/7)
  21. Bibliography (4/7)
  22. Bibliography (5/7)
  23. Bibliography (6/7)
  24. Bibliography (7/7)

Product information

  • Title: Handbook of Product Graphs, 2nd Edition
  • Author(s): Richard Hammack, Wilfried Imrich, Sandi Klavžar
  • Release date: June 2011
  • Publisher(s): CRC Press
  • ISBN: 9781439813058