ABSTRACT
The idea of family tree is very old, so it’s surprising that mathematicians didn’t adapt it for mathematical use until the 19th century. Nowadays, they’re used very widely, both in the form favored by genealogists and in a generalized form. As the definition below shows, trees are simply a special kind of graph. A node of a tree in graph theory can have any number of “parents” while in a family tree two is typical. Also, there cannot be any inbreeding in a mathematical tree. In mathematical terms, this means that there can be no cycles. A few examples of trees are shown below. Note that trees can be drawn in various orientations. The problem in chemistry that inspired Arthur Cayley to make use of trees was that of isomers. These are compounds that have the same chemical formula but possess different physical properties, due to differing arrangements of the atoms in the molecule.
