“Weakly Binary Tree”的概念、定义、习题解题方法及翻译-数学辞典

单词

Weakly Binary Tree

释义

Weakly Binary Tree

N.B. A detailed on-line essay by S. Finchwas the starting point for this entry.

A Rooted Tree for which the Root is adjacent to at most two Vertices, and all nonroot Vertices are adjacent to at most three Vertices. Let be the number of weakly binary trees of order , then . Let

(1)

where

			(2)
			(3)
			(4)
			(5)

Otter (Otter 1948, Harary and Palmer 1973, Knuth 1969) showed that

(6)

where

(7)

is the unique Positive Root of

(8)

and

(9)

is also given by

(10)

where

is given by

			(11)
			(12)

giving

(13)

References

Finch, S. ``Favorite Mathematical Constants.'' http://www.mathsoft.com/asolve/constant/otter/otter.html

Harary, F. Graph Theory. Reading, MA: Addison-Wesley, 1969.

Harary, F. and Palmer, E. M. Graphical Enumeration. New York: Academic Press, 1973.

Knuth, D. E. The Art of Computer Programming, Vol. 1: Fundamental Algorithms, 2nd ed. Reading, MA: Addison-Wesley, 1973.

Otter, R. ``The Number of Trees.'' Ann. Math. 49, 583-599, 1948.

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