Strongly Binary Tree


A strongly binary tree is a rooted tree for which the root is adjacent to either zero or two vertices, and all non-root vertices are adjacent to either one or three vertices (Finch 2003, p. 298). The numbers of strongly binary trees on n=1, 2, ... nodes are 1, 0, 1, 0, 1, 0, 2, 0, 3, 0, 6, 0, ... (OEIS A001190). The counts are 0 for n even, and g_k for odd n=2k+1, where g_n is the number of weakly binary trees on n nodes (Finch 2003, p. 298).

See also

Binary Tree, Complete Binary Tree, Rooted Tree, Weakly Binary Tree

Explore with Wolfram|Alpha


Finch, S. R. Mathematical Constants. Cambridge, England: Cambridge University Press, 2003.Sloane, N. J. A. Sequence A001190/M0790 in "The On-Line Encyclopedia of Integer Sequences."

Referenced on Wolfram|Alpha

Strongly Binary Tree

Cite this as:

Weisstein, Eric W. "Strongly Binary Tree." From MathWorld--A Wolfram Web Resource.

Subject classifications