The expected values and limiting behaviours for the Gutman index, Schultz index, multiplicative degree-Kirchhoff index and additive degree-kirchhoff index of a random cyclooctane chain

TL;DR

This paper derives explicit formulas for expected values and variances of several topological indices in random cyclooctane chains, showing they follow normal distribution asymptotically, and extends these results to related Kirchhoff indices.

Contribution

It provides the first explicit formulas and asymptotic normality results for multiple topological indices in random cyclooctane chains.

Findings

Explicit formulas for expected values of Gutman and Schultz indices.

Variances of these indices are determined and shown to be asymptotically normal.

Results extend to Kirchhoff indices with similar asymptotic behavior.

Abstract

In this paper, we first introduce the explicit analytical formulas for the expected values of the Gutman and Schultz indices for a random cyclooctane chain COCn. Meanwhile, the explicit formulas of the variances of the Gutman and Schultz indices for a random cyclooctane chain are determined and we prove these two indices are asymptotically subject to normal distribution. Furthermore, we are surprised to find the variances of Kf*(COCn) and Kf+(COCn) for a random cyclooctane chain based on the known results of others' paper and they are asymptotically subject to normal distribution.