Handbook of Product Graphs, Second Edition (Discrete Mathematics and Its Applications)

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: <ul>
<li>Cancellation results </li> <li>A quadratic recognition algorithm for partial cubes </li> <li>Results on the strong isometric dimension </li> <li>Computing the Wiener index via canonical isometric embedding </li> <li>Connectivity results </li> <li>A fractional version of Hedetniemi’s conjecture </li> <li>Results on the independence number of Cartesian powers of vertex-transitive graphs </li> <li>Verification of Vizing’s conjecture for chordal graphs </li> <li>Results on minimum cycle bases </li> <li>Numerous selected recent results, such as complete minors and nowhere-zero flows </li> </ul> 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.

Handbook of Product Graphs (Discrete Mathematics and Its Applications)

Computers & Technology

Richard Hammack

Sandi Klavzar

Wilfried Imrich

Operating Systems

CRC-Press

The Tower of Hanoi – Myths and Maths

This is the first comprehensive monograph on the mathematical theory of the solitaire game “The Tower of Hanoi” which was invented in the 19th century by the French number theorist Édouard Lucas. The book comprises a survey of the historical development from the game’s predecessors up to recent research in mathematics and applications in computer science and psychology. Apart from long-standing myths it contains a thorough, largely self-contained presentation of the essential mathematical facts with complete proofs, including also unpublished material. The main objects of research today are the so-called Hanoi graphs and the related Sierpiński graphs. Acknowledging the great popularity of the topic in computer science, algorithms and their correctness proofs form an essential part of the book. In view of the most important practical applications of the Tower of Hanoi and its variants, namely in physics, network theory, and cognitive (neuro)psychology, other related structures and puzzles like, e.g., the “Tower of London”, are addressed. Numerous captivating integer sequences arise along the way, but also many open questions impose themselves. Central among these is the famed Frame-Stewart conjecture. Despite many attempts to decide it and large-scale numerical experiments supporting its truth, it remains unsettled after more than 70 years and thus demonstrates the timeliness of the topic. Enriched with elaborate illustrations, connections to other puzzles and challenges for the reader in the form of (solved) exercises as well as problems for further exploration, this book is enjoyable reading for students, educators, game enthusiasts and researchers alike.

Andreas M. Hinz

Uros Milutinovic

Ciril Petr

Programming

Birkhauser

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Books by Sandi Klavzar