Trivalent Tree
A trivalent tree, also called a 3-valent tree or a 3-Cayley tree, is a tree for which each node has vertex degree
. The numbers of trivalent trees on 
, 2, ... nodes
are 1, 1, 1, 1, 2, 2, 4, 6, 11, 18, 37, 66, 135, 265, 552, ... (OEIS A000672).
The number of trees with nodes of valency either 1 or 3 for 
, 2, ... are
1, 1, 0, 1, 0, 1, 0, 1, 0, 2, 0, 2, 0, 4, ... (OEIS A052120).
These are sometimes called boron trees, since such a tree with 
nodes has
nodes of valency 3 (corresponding to boron atoms)
and 
nodes of valency (corresponding to
hydrogen atoms) for 
, 4, ....
Contact the MathWorld Team
acyclic graph
