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LEADER 00000cam a2200673Ma 4500
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008 140320s2011 flua ob 000 0 eng d
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020 9781439813058
020 1439813051
020 |q(hardcover ;|qalk. paper)
020 |q(paperback)
024 7 10.1201/b10959|2doi
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082 04 511.52
082 04 511.52
099 eBook O’Reilly for Public Libraries
100 1 Hammack, Richard H.
245 10 Handbook of product graphs /|cRichard Hammack, Wilfried
Imrich, Sandi Klavžar.|h[O'Reilly electronic resource]
250 2nd ed.
260 Boca Raton, FL :|bCRC Press,|c©2011.
300 1 online resource (xviii, 498 pages) :|billustrations
336 text|btxt|2rdacontent
337 computer|bc|2rdamedia
338 online resource|bcr|2rdacarrier
490 1 Discrete mathematics and its applications
504 Includes bibliographical references (pages 465-498).
505 0 |6880-01|aFront 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.
520 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.
590 O'Reilly|bO'Reilly Online Learning: Academic/Public
Library Edition
650 0 Graph theory.
650 7 Graph theory|2fast
700 1 Klavžar, Sandi,|d1962-|1https://id.oclc.org/worldcat/
entity/E39PBJhmMDMCr3TC3JdYjtt3Qq
700 1 Imrich, Wilfried,|d1941-|1https://id.oclc.org/worldcat/
entity/E39PBJw4yp3TgTh7XJtHFrt7pP
776 08 |iPrint version:|aHammack, Richard.|tHandbook of Product
Graphs, Second Edition.|dBaton Rouge : CRC Press, ©2011
|z9781439813041
830 0 Discrete mathematics and its applications.
856 40 |uhttps://ezproxy.naperville-lib.org/login?url=https://
learning.oreilly.com/library/view/~/9781439813058/?ar
|zAvailable on O'Reilly for Public Libraries
880 0 |6505-01/(S|aFront 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.
938 Askews and Holts Library Services|bASKH|nAH21638392
938 YBP Library Services|bYANK|n15920077
938 YBP Library Services|bYANK|n3652028
938 ebrary|bEBRY|nebr10502498
938 CRC Press|bCRCP|nCRC0KE10613PDF
994 92|bJFN