Probabilistic Methods in the Study of Topological Indices on Random Spider Trees

Abstract

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