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

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 COC n . 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 * (COC n ) and Kf + (COC n ) for a random cyclooctane chain based on the known results of others' paper and they are asymptotically subject to normal distribution.