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

TL;DR

This paper analyzes the structure and topological indices of random spider trees using probabilistic methods, providing exact and asymptotic distributions, and relating the model to preferential attachment processes.

Contribution

It introduces a probabilistic framework for characterizing topological indices of random spider trees and derives their distributions, connecting to preferential attachment models.

Findings

Exact distribution of leaves in RSTs

Asymptotic behavior of topological indices

Connection to preferential attachment models

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.