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Handbook of product graphs / Richard Hammack, Wilfried Imrich, Sandi Klavzar.
- Format:
- Book
- Author/Creator:
- Hammack, Richard H.
- Series:
- Discrete mathematics and its applications.
- Discrete mathematics and its applications
- Language:
- English
- Subjects (All):
- Graph theory.
- Combinatorial analysis.
- Physical Description:
- 1 online resource (518 p.)
- Edition:
- 2nd ed.
- Place of Publication:
- Boca Raton, FL : CRC Press, c2011.
- Language Note:
- English
- System Details:
- text file
- 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 dimen
- 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 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 TheoremsIV. 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 ResultsVI. Related Concepts; 31. Infinite Graphs; 32. Products of Digraphs; 33. Near Products; Appendix: Hints and Solutions to Exercises; Bibliography
- Notes:
- A Chapman & Hall book.
- Includes bibliographical references and indexes.
- ISBN:
- 9786613311528
- 9780429130595
- 0429130597
- 9781283311526
- 1283311526
- 9781439813058
- 1439813051
- OCLC:
- 744521234
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