n阶树的指数分布

Exponent Set of Trees with n Venices

设Ｔｎ表示全体ｎ阶树所构成的集合，记Ｔ（ｎ，ｄ）＝｛Ｔ∈Ｔｎ．｜Ｔ中恰有ｄ（≥１）个环｝．本文证明了Ｔ（ｎ，ｄ）的本原指数集合Ｓｎｄ为：（ｄ≥２）．并且证明了Ｔ（ｎ，ｄ）的暴敛指数集Ｓｎ＝｛２，３，……，ｎ－１｝．进一步刻划了Ｔ（ｎ，ｄ）中本原指数达到Ｚｎ—４，Ｚｎ—２的树的特征．

Let Tn denote the set of all trees of order n. Let T(n,d) = {T∈Tn| The sum of all loops in T is d (≥1)}. In this paper, we prove that the set Sn,d of primitive exponent of T(n,d) is:And we prove that the set Sn of convergence index of T(n,d) is:Moreover, we also obtain a characterization of the primitive tree whose exponents equal to 2n-4 and 2n-2.