A Cayley tree is a tree in which each non-leaf graph vertex has a constant number of branches 
is called an 
-Cayley tree. 2-Cayley trees are path
graphs. The unique 
-Cayley
tree on 
nodes is the star graph. The illustration above shows
the first few 3-Cayley trees (also called trivalent trees, binary trees, or boron
trees). The numbers of binary trees on 
, 2, ... nodes (i.e., 
-node trees having vertex degree
either 1 or 3; also called 3-Cayley trees, 3-valent trees, or boron trees) are 1,
1, 0, 1, 0, 1, 0, 1, 0, 2, 0, 2, 0 ,4, 0, 6, 0, 11, ... (OEIS A052120).
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The illustrations above show the first few 4-Cayley and 5-Cayley trees.
The percolation threshold for a Cayley tree having 
branches is
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