Topological indices in Random Spiro Chains

TL;DR

This paper analyzes topological indices in random spiro chains using a martingale approach, deriving explicit formulas for their distribution, expectation, variance, and asymptotic normality, including specific indices like Nirmala, Sombor, Randic, and Zagreb.

Contribution

It provides the first explicit analytical expressions and asymptotic normality results for topological indices in random spiro chains, enhancing understanding of their probabilistic behavior.

Findings

Explicit formulas for distribution, expectation, and variance of indices.

Asymptotic normality of indices as chain length increases.

Comparison of different topological indices in random spiro chains.

Abstract

In this paper, we study topological indices in random spiro chains via a martingale approach. In which their explicit analytical expressions of the exact distribution, expected value and variance are obtained. As n goes to infinity, the asymptotic normality of topological indices of a random spiro chain is established through the Martingale Central Limit Theorem. In particular, we compute the Nirmala, Sombor, Randic and Zagreb index for a random spiro chain along with their comparative analysis.