Have you ever seen the movie Good Will Hunting? There was this genius who solved an apparently easy problem in tree generation, stated in the following sentence:
Draw all homeomorphically irreducible trees with n = 10.
The problem itself may be quite easy, but how would you prove that there are exactly 10 trees? How about the problem where you have to prove the number of these trees with n = 20?
The book Tree generation and enumeration: An extended model in graph theory tackles this challenge by creating a mathematical system in tree generation and enumeration with its own language and algorithms. The scope of tree generation is also broadened to equations, a branch in graph theory called advanced vertex edge algebra.
If you have ever wondered if trees, natural numbers and partitions have something in common, then this book has something in store for you!