Cayley's formula

The Cayley 's formula ( named after Arthur Cayley ), sometimes called Cayley, is a set of the enumerative combinatorics. He says that there are several designated trees with nodes.

Formulations

• There are several marked trees with nodes.
• The designated complete graph with nodes has different spanning trees.

Evidence

For the Cayley formula, there are countless proofs, some of which are considered by many mathematicians as particularly beautiful. This is reflected inter alia in the fact that the Cayley formula is a chapter in Proofs from THE BOOK. There are four different proofs are presented:

History

The formula was first published by Carl Wilhelm Borchardt (1860 ). 1889 extended the Cayley formula and formulated in graph terminology, which is why it has since been associated with his name.

Also worth noting that James Joseph Sylvester already ( 1857) published an equivalent result.