Abstract In this study, we characterize the structure and some topological indices of a class random spider trees (RSTs) such as degree-based Gini index, Hoover generalized Zagreb other associated with these. We obtain exact asymptotic distributions number leaves via probabilistic methods. Moreover, relate model to RSTs that evolves in preferential attachment manner.

Kazemi (2014) introduced a new version of bucket recursive trees as another generalization of recursive trees where buckets have variable capacities. In this paper, we get the $p$-th factorial moments of the random variable $S_{n,1}$ which counts the number of subtrees size-1 profile (leaves) and show a phase change of this random variable. These can be obtained by solving a first order partial...