Handbook of Product Graphs

ISBN-13: 9781138199088 / Angielski / Miękka / 2016 / 536 str.

Richard Hammack; Wilfried Imrich; Sandi Klav Ar

Opis

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."

Recenzje

It is my pleasure to introduce you to the marvelous world of graph products, as presented by three experts in a hugely expanded and updated edition of the classic by Imrich and Klavžar. This version, really a new book (thirty-three chapters, up from nine!), contains streamlined proofs, new applications, solutions to conjectures (such as Vizing’s conjecture for chordal graphs), and new results in graph minors and flows. Every graph theorist, most combinatorialists, and many other mathematicians will want this volume in their collection. …The authors have paid careful attention to algorithmic issues (indeed, many of the most attractive algorithms are products of their own research). Readers will find a gentle but incisive introduction to graph algorithms here, and a persuasive lesson on the insights to be gained by algorithmic analysis. In sum—and product—Hammack, Imrich, and Klavžar have put together a world of elegant and useful results in a cogent, readable text. The old book was already a delight, and you will want the new one in an accessible place on your bookshelf.
—From the Foreword by Peter Winkler, Dartmouth College, Hanover, New Hampshire, USA

Spis treści

A Brief Introduction to Graphs and Their Products. Factorization and Cancellation. Isometric Embeddings. Algorithms. Invariants. Related Concepts. Appendix. Bibliography. Indices.