Handbook of Mathematical Induction: Theory and Applications shows how to find and write proofs via mathematical induction. This comprehensive book covers the theory, the structure of the written proof, all standard exercises, and hundreds of application examples from nearly every area of mathematics.

In the first part of the book, the author discusses different inductive techniques, including well-ordered sets, basic mathematical induction, strong induction, double induction, infinite descent, downward induction, and several variants. He then introduces...

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...

This book provides an introduction and overview of the growing area of chip-firing. It offers an appreciation for the richness and diversity of chip-firing. Chip-firing refers to a discrete dynamical system -- a commodity is exchanged between sites of a network according to very simple local rules. Although governed by local rules, the long-term global behavior of the system reveals fascinating properties. Working over the simplest type of network, basic properties are covered from a variety of perspectives. This gives the reader both a broad context of the field and concrete entry points...