TOPICS
Search

Trivalent Tree


TrivalentTree

A trivalent tree, also called a 3-valent tree or a 3-Cayley tree, is a tree for which each node has vertex degree <=3. The numbers of trivalent trees on n=1, 2, ... nodes are 1, 1, 1, 1, 2, 2, 4, 6, 11, 18, 37, 66, 135, 265, 552, ... (OEIS A000672).

TrivalentTree13

The number of trees with nodes of valency either 1 or 3 for n=1, 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 t=2n+2 nodes has n nodes of valency 3 (corresponding to boron atoms) and n+2 nodes of valency (corresponding to hydrogen atoms) for t=2, 4, ....


See also

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

Explore with Wolfram|Alpha

References

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

Referenced on Wolfram|Alpha

Trivalent Tree

Cite this as:

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

Subject classifications