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# Tree Leaf

A leaf of an unrooted tree is a node of vertex degree 1. Note that for a rooted or planted tree, the root vertex is generally not considered a leaf node, whereas all other nodes of degree 1 are.

A function to return the leaves of a tree may be implemented in a future version of the Wolfram Language as LeafVertex[g].

The following tables gives the total numbers of leaves for various classes of graphs on , 2, ... nodes. Note that for rooted and planted trees, the root vertex is generally not counted as a leaf, even if it has vertex degree 1.

 graph type OEIS leaf count for , 2, ... nodes graph A055540 0, 2, 4, 14, 38, 153, 766, 6259, 88064, ... labeled graph A095338 0, 2, 12, 96, 1280, 30720, ... labeled tree A055541 0, 2, 6, 36, 320, 3750, ... planted tree A003227 0, 1, 1, 3, 8, 22, 58, 160, 434, 1204, 3341, 9363, ... planted tree including root nodes A095339 0, 2, 2, 5, 12, 31, 78, 208, 549, 1490, 4060, 11205, ... rooted tree A003227 0, 1, 1, 3, 8, 22, 58, 160, 434, 1204, 3341, 9363, ... rooted tree including degree-1 root nodes A095337 0, 2, 4, 10, 26, 67, 180, 482, 1319, 3627, 10082, 28150, ... tree A003228 0, 2, 2, 5, 9, 21, 43, 101, ...

Branch, Child, Fork, Maximum Leaf Number, Minimum Leaf Number, Root Vertex, Tree, Tree Height

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## References

Robinson, R. W. and Schwenk, A. J. "The Distribution of Degrees in a Large Random Tree." Discr. Math. 12, 359-372, 1975.Slater, P. J. "Leaves of Trees." In Proceedings of the Sixth Southeastern Conference on Combinatorics, Graph Theory and Computing, (Utilitas Mathematics) (Ed. F. Hoffman et al. ) Winnipeg, pp. 549-559, 1975.Sloane, N. J. A. Sequences A003227/M2744, A003228/M0351, A055540, A055541, A095337, A095338, and A095339 in "The On-Line Encyclopedia of Integer Sequences."

Tree Leaf

## Cite this as:

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