Handbook of Product Graphs

ISBN-13: 9781439813041 / Angielski / Twarda / 2011 / 536 str.

Richard Hammack; Wilifred Imrich; Sandi Klavzar

Opis

Now in its second edition, this book provides the first comprehensive account of the four standard products of graphs. It systematically treats the Cartesian, strong, direct, and lexicographic product of graphs and graphs isometrically embeddable into them. The text collects a wealth of information previously widely scattered in the literature on products of graphs, in particular, information on hypercubes, median graphs, Hamming graphs, triangle-free graphs, and vertex-transitive graphs. It also covers colorings, automorphisms, homomorphisms, domination, the capacity of products of graphs, as well as applications to chemical graph theory and computational biology.

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.