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Divisors and sandpiles. An introduction to chip-firing. (English) Zbl 1411.05003
Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-4218-7/pbk; 978-1-4704-4861-5/ebook). xiv, 325 p. (2018).
This is a well-written book about chip-firing in graphs, graph divisors and sandpile models and their many connections with various branches of mathematics. I am not familiar with this subject and what surprised me while reading the book was the number of areas it is related to. Deep connections with graph theory, group theory, theory of algorithms and geometry have been discussed in this book, and for sure there are deeper connections to be explored in the future.
Prerequisites for reading the book are basic courses in linear and abstract algebra, and it is aimed at advanced undergraduate students. Indeed, the authors have already taught several courses based on this material in undergraduate liberal arts colleges in the US. The book also introduces some generally useful mathematics that lies at the edge of the standard mathematics curriculum. All the concepts have been defined very well and accompanied with examples, hence it is also a perfect self-study book for anyone interested in these fascinating areas.
For a description of material covered, please refer to the book cover.

05-02 Research exposition (monographs, survey articles) pertaining to combinatorics
05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
05C05 Trees
05C85 Graph algorithms (graph-theoretic aspects)