TOPICS

# 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, ....

Binary Tree, Cayley Tree, Strongly Binary Tree, Tree, Weakly Binary Tree

## Explore with Wolfram|Alpha

More things to try:

## References

Sloane, N. J. A. Sequences A000672/M0326 and A052120 in "The On-Line Encyclopedia of Integer Sequences."

Trivalent Tree

## Cite this as:

Weisstein, Eric W. "Trivalent Tree." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/TrivalentTree.html