Degree Based Topological Indices of a General Random Chain

TL;DR

This paper analyzes degree-based topological indices of various random chains, deriving explicit formulas and asymptotic behaviors, providing a unified framework for understanding their properties in complex molecular structures.

Contribution

It introduces a unified approach to study degree-based topological indices of random chains, including explicit formulas and asymptotic analysis for several indices.

Findings

Explicit expressions for expected values and variances of indices.

Asymptotic behavior of topological indices established.

Analysis covers various types of random chains.

Abstract

In this paper, we examine a specific type of random chains and propose an unified approach to studying the degree-based topological indices, including their extreme values. We derive explicit analytical expressions for the expected values and variances of these indices and we establish the asymptotic behavior of the indices. Specifically, we analyze the first Zagreb index, Sombor index, Harmonic index, Geometric-Arithmetic index, Inverse Sum Index, and the second Zagreb index for various general random chains, including random phenylene, random polyphenyl, random hexagonal, and linear chains.