Product Graphs. Structure And Recognition

Addressing the growing usefulness of current methods for recognizing product graphs, this new work presents a much-needed, systematic treatment of the Cartesian, strong, direct, and lexicographic products of graphs as well as graphs isometrically embedded into them. Written by two leading experts in this rapidly evolving area of combinatorics, "Product Graphs : Structure and Recognition" compiles and consolidates a wealth of information previously scattered throughout the literature, providing researchers in the field with ready access to numerous recent results as well as several new recognition algorithms and proofs. The authors explain all topics from the ground up and make the requisite theory and data structures easily accessible for mathematicians and computer scientists alike. Coverage includes the basic algebraic and combinatorial properties of product graphs. Hypercubes, median graphs, Hamming graphs, triangle-free graphs, and vertex-transitive graphs. Colorings, automorphisms, homomorphisms, domination, and the capacity of products of graphs. Sample applications, including novel applications to chemical graph theory. Proofs and algorithms presented at varying levels of difficulty. Clear connections to other areas of graph theory. Figures, exercises, and hundreds of references.