Editing Cayley's formula (section)

==Proof==
Many proofs of Cayley's tree formula are known.<ref>{{Cite book
 | last1 = Aigner | first1 = Martin | author1-link = Martin Aigner
 | last2 = Ziegler | first2 = Günter M. | author2-link = Günter M. Ziegler
 | pages = 141–146
 | publisher = [[Springer-Verlag]]
 | title = Proofs from THE BOOK
 | year = 1998| title-link = Proofs from THE BOOK }}</ref>
One classical proof of the formula uses [[Kirchhoff's matrix tree theorem]], a formula for the number of spanning trees in an arbitrary graph involving the [[determinant]] of a [[matrix (mathematics)|matrix]].  [[Prüfer sequence]]s yield a [[bijective proof]] of Cayley's formula. Another bijective proof, by [[André Joyal]], finds a one-to-one transformation between ''n''-node trees with two distinguished nodes and maximal directed [[pseudoforest]]s.
A proof by [[double counting (proof technique)|double counting]] due to Jim Pitman counts in two different ways the number of different sequences of directed edges that can be added to an [[Null graph|empty graph]] on n vertices to form from it a rooted tree; see {{section link|Double counting (proof technique)|Counting trees}}.