Handbook of Product Graphs, Second Edition

Richard Hammack, Wilfried Imrich, Sandi Klavžar

June 6, 2011 by CRC Press
Reference - 536 Pages - 75 B/W Illustrations
ISBN 9781439813041 - CAT# K10662
Series: Discrete Mathematics and Its Applications


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  • Offers a thorough introduction to the Cartesian, strong, direct, and lexicographic products and their subgraphs
  • Presents numerous new results and algorithms, including some that solve long-standing questions
  • Illustrates applications of graph products in several areas, including dynamic location theory, chemistry, human genetics, structural mechanics, and graph visualization
  • Describes the dot product, the random dot product, and applications to the generation of random graphs with prescribed properties
  • Applies the free product of graphs to infinite median graphs
  • Defines the zig-zag and replacement products
  • Contains well over 300 exercises, with hints or full solutions in the appendix
  • Provides sample implementations of selected algorithms and other useful information on the book’s website


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.


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