| Description |
1 online resource (xviii, 498 pages) : illustrations |
| Series |
Discrete mathematics and its applications |
|
Discrete mathematics and its applications.
|
| Bibliography |
Includes bibliographical references (pages 465-498). |
| Summary |
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 presents full proofs of many important results as well as up-to-date research and conjectures. Results and Algorithms New to the Second Edition: Cancellation results A quadratic recognition algorithm for partial cubes Results on the strong isometric dimension Computing the Wiener index via canonical isometric embedding Connectivity results A fractional version of Hedetniemi's conjecture Results on the independence number of Cartesian powers of vertex-transitive graphs Verification of Vizing's conjecture for chordal graphs Results on minimum cycle bases Numerous selected recent results, such as complete minors and nowhere-zero flows The second edition of this classic handbook provides a thorough introduction to the subject and an extensive survey of the field. The first three parts of the book cover graph products in detail. The authors discuss algebraic properties, such as factorization and cancellation, and explore interesting and important classes of subgraphs. The fourth part presents algorithms for the recognition of products and related classes of graphs. The final two parts focus on graph invariants and infinite, directed, and product-like graphs. Sample implementations of selected algorithms and other information are available on the book's website, which can be reached via the authors' home pages. |
| Contents |
Front Cover -- Contents -- Foreword -- Preface -- I.A Brief Introduction to Graphs and Their Products -- 1. Graphs -- 2. Automorphisms and Invariants -- 3. Hypercubes and Isometric Subgraphs -- 4. Graph Products -- 5. The Four Standard Graph Products -- II. Factorization and Cancellation -- 6. Cartesian Product -- 7. Strong Product -- 8. Direct Product -- 9. Cancellation -- 10. Lexicographic Product -- III. Isometric Embeddings -- 11. The Relation K and Partial Cubes -- 12. Median Graphs -- 13. The Canonical Isometric Embedding -- 14. A Dynamic Location Problem -- 15. Isometries in Strong Products and Product Dimensions -- 16. Fixed Box Theorems -- IV. Algorithms -- 17. Graph Representation and Algorithms -- 18. Recognizing Hypercubes and Partial Cubes -- 19. Chemical Graphs and the Wiener Index -- 20. Arboricity, Squares, and Triangles -- 21. Recognizing Median Graphs -- 22. Recognizing Partial Hamming Graphs and Quasi-Median Graphs -- 23. Factoring the Cartesian Product -- 24. Recognizing Direct, Strong, and Lexicographic Products -- V. Invariants -- 25. Connectivity -- 26. Coloring and Hedetniemi's Conjecture -- 27. Independence Number and Shannon Capacity -- 28. Domination and Vizing's Conjecture -- 29. Cycle Spaces and Bases -- 30. Selected Results -- VI. Related Concepts -- 31. Infinite Graphs -- 32. Products of Digraphs -- 33. Near Products -- Appendix: Hints and Solutions to Exercises -- Bibliography. |
|
Front Cover -- Contents -- Foreword -- Preface -- I.A Brief Introduction to Graphs and Their Products -- 1. Graphs -- 2. Automorphisms and Invariants -- 3. Hypercubes and Isometric Subgraphs -- 4. Graph Products -- 5. The Four Standard Graph Products -- II. Factorization and Cancellation -- 6. Cartesian Product -- 7. Strong Product -- 8. Direct Product -- 9. Cancellation -- 10. Lexicographic Product -- III. Isometric Embeddings -- 11. The Relation Θ and Partial Cubes -- 12. Median Graphs -- 13. The Canonical Isometric Embedding -- 14. A Dynamic Location Problem -- 15. Isometries in Strong Products and Product Dimensions -- 16. Fixed Box Theorems -- IV. Algorithms -- 17. Graph Representation and Algorithms -- 18. Recognizing Hypercubes and Partial Cubes -- 19. Chemical Graphs and the Wiener Index -- 20. Arboricity, Squares, and Triangles -- 21. Recognizing Median Graphs -- 22. Recognizing Partial Hamming Graphs and Quasi-Median Graphs -- 23. Factoring the Cartesian Product -- 24. Recognizing Direct, Strong, and Lexicographic Products -- V. Invariants -- 25. Connectivity -- 26. Coloring and Hedetniemi's Conjecture -- 27. Independence Number and Shannon Capacity -- 28. Domination and Vizing's Conjecture -- 29. Cycle Spaces and Bases -- 30. Selected Results -- VI. Related Concepts -- 31. Infinite Graphs -- 32. Products of Digraphs -- 33. Near Products -- Appendix: Hints and Solutions to Exercises -- Bibliography. |
| Subject |
Graph theory.
|
|
Graph theory |
| Added Author |
Klavžar, Sandi, 1962-
|
|
Imrich, Wilfried, 1941-
|
| Other Form: |
Print version: Hammack, Richard. Handbook of Product Graphs, Second Edition. Baton Rouge : CRC Press, ©2011 9781439813041 |
| ISBN |
9781439813058 |
|
1439813051 |
|
(hardcover ; alk. paper) |
|
(paperback) |
| Standard No. |
10.1201/b10959 doi |
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