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Asymptotic formulas for the enumerator of trees with a given number of hanging or internal vertices

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Abstract

Let t(r, n) be the number of trees with n vertices of which r are hanging and q are internal (r=n−9). For a fixed r or q we prove the validity of the asymptotic formulas (r > 2)t(r, n)≈t/r¦(r−2)¦ 22−r n 2r−4 (n→∞)t(n−q, n)≈1/q¦(q−1)¦q q−2 n q−1 (n→∞) In the derivation of these formulas we do not use the expression for the enumerator of the trees with respect to the number of hanging vertices.

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Authors and Affiliations

  1. State Scientific-Research and Design Institute for the Varnish and Paint Industry, USSR

    V. A. Voblyi

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  1. V. A. Voblyi
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Translated from Matematicheskie Zametki, Vol. 21, No. 1, pp. 65–70, January, 1977.

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Voblyi, V.A. Asymptotic formulas for the enumerator of trees with a given number of hanging or internal vertices. Mathematical Notes of the Academy of Sciences of the USSR 21, 36–39 (1977). https://doi.org/10.1007/BF02317033

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  • DOI: https://doi.org/10.1007/BF02317033

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