Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6417583 | Journal of Mathematical Analysis and Applications | 2016 | 11 Pages |
Abstract
Let Tn denote the set of trees with n vertices. Suppose that each tree in Tn is equally likely. We show that the number of non-isomorphic rooted trees obtained by rooting a tree equals (μr+o(1))n for almost every tree of Tn, where μr is a constant. As an application, we show that in Tn the number of any given pattern, which is a fixed small tree with internal vertices specified, is asymptotically normally distributed with mean â¼Î¼Mn and variance â¼ÏMn, where μM and ÏM are some constants related to the given pattern. This solves an open question claimed in Kok's thesis.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Xueliang Li, Yiyang Li, Yongtang Shi,