Handbook of Product Graphs

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.

Richard Hammack is an associate professor in the Department of Mathematics and Applied Mathematics at Virginia Commonwealth University. Dr. Hammack is a member of the American Mathematical Society, the Mathematical Association of America, and the Institute of Combinatorics and its Applications. He earned a Ph.D. in mathematics from the University of North Carolina at Chapel Hill.

Wilfried Imrich is professor emeritus in the Department of Mathematics and Information Technology at Montanuniversität Leoben. His research interests include the structure of finite and infinite graphs, graph automorphisms, combinatorial group theory, and graph algorithms. Dr. Imrich earned a Ph.D. from the University of Vienna.

Sandi Klavžar is a professor in the Faculty of Mathematics and Physics at the University of Ljubljana and in the Faculty of Natural Sciences and Math at the University of Maribor. Dr. Klavžar is an editorial board member of Ars Mathematica Contemporanea, Asian-European Journal of Mathematics, Discussiones Mathematicae Graph Theory, European Journal of Combinatorics, and MATCH Communications in Mathematical and in Computer Chemistry.