On The Bipartition Numbers Of Random Trees, $II$

Abstract

Let $T_n$ denote any rooted tree with $n$ nodes and let $p=p(T_n)$ and $q=q(T_n)$ denote the number of nodes at even and odd distance, respectively, from the root. We investigate the limiting distribution, expected value, and variance of the numbers $D(T_n)=|p–q|$ when the trees $T_n$ belong to certain simply generated families of trees.