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

Jia-Bao Liu; Jiao-Jiao Gu; Kang Wang

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arXiv · 2203.12923

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

Jia-Bao Liu·Jiao-Jiao Gu·Kang Wang

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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.

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Jia-Bao Liu, Jiao-Jiao Gu, Kang Wang. 2022-03-24. 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. https://arxiv.org/abs/2203.12923

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