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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