Several topological indices of random caterpillars

TL;DR

This paper studies the properties of random caterpillar trees, a model for molecular structures, by analyzing various topological indices and establishing a central limit theorem for the Zagreb index.

Contribution

It introduces the concept of random caterpillars and derives their topological indices, including a new central limit theorem for the Zagreb index.

Findings

Derived formulas for Zagreb, Randić, and Wiener indices of random caterpillars.

Established a central limit theorem for the Zagreb index.

Provided insights into the molecular structure modeling using random graph theory.

Abstract

In chemical graph theory, caterpillar trees have been an appealing model to represent the molecular structures of benzenoid hydrocarbon. Meanwhile, topological index has been thought of as a powerful tool for modeling quantitative structure-property relationship and quantitative structure-activity between molecules in chemical compounds. In this article, we consider a class of caterpillar trees that are incorporated with randomness, called random caterpillars, and investigate several popular topological indices of this random class, including Zagreb index, Randi\'{c} index and Wiener index, etc. Especially, a central limit theorem is developed for the asymptotic distribution of the Zagreb index of random caterpillars.